Kyiv and Lviv, Ukraine CNN  — 

Russian forces fired rockets at a TV tower in the Ukrainian capital of Kyiv on Tuesday, hours after Moscow warned of strikes on other facilities linked to Ukrainian security agencies.

The rocket attack took out broadcasting hardware, raising fears that Moscow is attempting to knock out the city’s communications infrastructure. Ahead of the strikes, Russia’s military urged nearby residents to flee.

The attack, along with a beef-up of assaults on other key cities, brings the Russian invasion right into the heart of the nation.

Another rocket hit a private maternity clinic near the capital Kyiv on Tuesday, leaving the clinic damaged but still standing, according to the Adonis maternity clinic chief Vitaliy Gyrin’s Facebook post. Separately, a military strike tore through two apartment blocks in a town west of Kyiv.

As the rockets hit Kyiv on Tuesday, a 40-mile Russian convoy of tanks, armored vehicles and towed artillery was headed toward the Ukrainian capital, according to satellite images from Maxar Technologies.

However, a US official said the convoy has been stalled due to fuel supply issues. The Russian advance on Kyiv remains “basically… where it was yesterday” according to a senior defense official, who also said there were signs that they were running out of food.

While Ukraine mounts a defense against the Russian onslaught, some 677,000 people have fled the country in “less than a week,” with 150,000 fleeing in the last 24 hours alone, according to the United Nations.

The UN has also raised concerns for the millions of people still in the country, with UN humanitarian chief Martin Griffiths saying this is the “darkest hour” for the people of Ukraine.

“Families with small children are hunkered down in basements and subway stations or running for their lives to the terrifying sound of explosions and wailing sirens,” he said in a statement.

In his State of the Union speech Tuesday, US President Joe Biden said President Vladimir Putin “badly miscalculated” when he invaded Ukraine and announced a ban on Russian aircraft from US airspace which he said would further isolate Russia and squeeze its economy.

He reiterated that US forces would not deploy to the Ukraine – instead, they were deployed to Europe to defend America’s NATO allies “in the event that Putin decides to keep moving west.”

In an exclusive interview with CNN and Reuters from a bunker ahead of the speech, Ukrainian President Volodymyr Zelensky reiterated calls for the US and NATO to establish a no-fly zone over Ukraine or put boots on the ground, saying “I do believe that leaders do have to support democratic countries and they have to help them.”

Asked if he felt Ukraine was wasting its time by talking with Russia, he said: “We’ll see.” On Monday, Ukrainian and Russian officials met for the first time since Moscow began their assault last week.

Biden and Zelensky held a 30-minute phone conversation on Tuesday. Biden, the White House said, “underscored the United States’ sustained help for Ukraine, including ongoing deliveries of security assistance, economic support, and humanitarian aid.”

Here’s what to know

  • Russia shifted to an aggressive bombing campaign, increasingly hitting civilians
  • Freedom Square in Ukraine’s second-largest city of Kharkiv was targeted by rockets, killing at least 10 people
  • The defensive line the southern city of Kherson fell and Russian troops were seen driving around
  • Leader of the self-declared separatist region in Donetsk says Russian-backed separatists plan to surround the port city of Mariupol
  • Ukrainian President Zelensky pleas for Ukraine’s immediate membership to the EU

The attack in Kyiv came just hours after the Russian military threatened to carry out strikes in Kyiv, though it said its targets were Ukrainian State Security Agency facilities and the country’s psychological operations unit, according to a statement reported by Russian state media TASS.

In videos and social media posts shared soon after the strike, plumes of smoke were seen swirling around the red-and-white steel TV tower building, which is located near the city’s Babyn Yar Holocaust Memorial Center (BYHMC).

The area surrounding a massive TV tower in Kyiv after being hit by military strikes on Tuesday.

In a statement, BYHMC said the remembrance site was struck by Russian forces. “Putin seeks to distort and manipulate the Holocaust to justify an illegal invasion of a sovereign democratic country is utterly abhorrent,” said BYHMC Advisory Board Chair Natan Sharanksy, adding that it is “symbolic” that the attack happened where an estimated 70,000 to 100,000 people were shot by the Nazis.

Russian forces also attacked key cities in Ukraine from several sides, scaling up its bombardment of Ukraine’s second-largest city, Kharkiv, in the northeast and breaking through a heavily contested port city in the south.

Russia’s actions on Tuesday mark a far less restrained bombing campaign, raising concerns that more civilians could be hit in strikes. The UN says that at least 102 civilians have been killed across the country and 304 injured, though those figures are likely to underestimate the true toll.

US officials also warned that the sheer breadth of Russian firepower could overwhelm Ukrainian resistance.

Russia’s military is far bigger and more powerful than Ukraine’s by just about every measure, but Ukraine’s allies, including the European Union, are scrambling to send more weapons into the country to aid its defense.

On Tuesday, Kyiv Mayor Vitali Klitschko warned that “the enemy is on the outskirts of the capital,” but the Ukrainian military is “preparing to defend Kyiv.”

“Fortifications and checkpoints have been built at the entrances to the city. I ask everyone to keep calm. Do not go outside unnecessarily and stay in shelters in case of alarm,” he said in a video message.

The Russian convoy is seen along with smoke rising from what appears to be burning homes, northwest of Invankiv, Ukraine.

In an interview with CNN Tuesday, Ukrainian Foreign Minister Dmytro Kuleba told CNN that Russia “dominates in the sky” while Ukrainian forces have sought to destroy ground forces headed towards Ukrainian cities.

“Our pilots are fighting fiercely against them, but we also have losses,” Kuleba said. “So the Russians use their fighting jets and bombers to attack our cities and we need to counter this threat.”

He added, “This are the two most urgent requests that we lodged with our partners.”

Zelensky’s plea

EU chief Ursula von der Leyen, left, applauds in Brussels as Ukrainian President Volodymyr Zelensky makes a speech.

President Zelensky made an impassioned plea to the European leaders earlier Tuesday to grant Ukraine immediate membership to the EU, saying his country was fighting for survival.

Zelensky’s plea came as Russia accelerated strikes on Kharkiv, which was rocked by a large explosion that incinerated cars, blew out windows and destroyed a large government building in the main Freedom Square.

Emergency services said at least 10 people were killed and 24 injured in the strike, which Zelensky described as an “act of terror” on civilians in a Facebook post.

Late Monday, at least five separate residential areas in Kharkiv were hit by rockets, according to CNN analysis of social media videos.

During a trip to Poland on Tuesday, UK Prime Minister Boris Johnson called the Russian invasion “worse than our predictions,” pointing to attacks like those seen in Kharkiv’s neighborhoods.

“It is clear that Vladimir Putin is prepared to use barbaric and indiscriminate tactics against innocent civilians to bomb tower blocks, to send missiles into tower blocks, to kill children, as we’re seeing in increasing numbers,” he said.

A Kharkiv resident named Tetyana, 66, told CNN that a shell hit her house early Tuesday morning, shattering its windows.

Tetyana – who sleeps in her shoes and coat since the invasion began – ran to her basement where her relative Oleg told her that his car had burned down and “the school in the yard was totally destroyed.”

This school was destroyed as a result of a fight not far from Kharkiv's city center on February 28.

The day before, CNN confirmed five residential areas in the city had been hit by military strikes on Monday using videos shared on social media.

Dramatic video, taken by a surveillance-type camera at an apartment complex on Velyka Kil’tseva St, shows repeated explosions from one strike that landed in a parking lot and walkway.

The intense shelling – at least eight explosions are seen but there are more heard – lasts for 20 seconds. As the munitions rain down, people are seen running as the explosions dot the ground: one individual falls to the ground as explosions surround them. A parked car explodes after taking a direct hit.

On Klochkivska Street, graphic videos shows blood and body parts outside of a small grocery store.

“It’s horrible, guys,” a voice in the video says. “Right in my part of the city. Boots and leg were removed, here’s parts of brain.”

Russian forces enter port city

Russian-backed forces have also made gains down South. In the port city of Kherson – west of Mariupol and north of the Crimean Peninsula, which Russia annexed in 2014 – Ukrainian defensive lines appear to have fallen and Russian military vehicles have been seen driving inside the city.

The leader of the self-declared separatist region in Donetsk said he expects his forces to surround Mariupol on Tuesday. The town of Volnovakha, half-way between Mariupol and Donetsk, was almost completely surrounded, Denis Pushilin added.

Ukraine has accused Russia of committing war crimes by targeting civilians, and on Monday, the International Criminal Court said it would open an investigation into Russia’s invasion of Ukraine – a move that was welcomed by Kyiv.

The Kremlin has denied the accusations, repeatedly saying it is not targeting civilian areas.

A humanitarian crisis

As bitter fighting takes place across the country, many Ukrainians are fleeing the country at a pace that could turn into “Europe’s largest refugee crisis this century,” the United Nations Refugee Agency (UNHCR) said Tuesday.

Some 677,000 people have fled Ukraine in “less than a week” with 150,000 having left in the last 24 hours alone, UNHCR’s deputy High Commissioner Kelly Clements said Tuesday. Clements said the UNHCR launched “emergency appeals” to donors for $1.7 billion in humanitarian support for people in Ukraine and refugees.

Many of them are women who have had to leave behind their fathers and husbands as men aged 18 to 60 are banned from leaving the country.

“Families with small children are hunkered down in basements and subway stations or running for their lives to terrifying sounds of explosions and wailing sirens,” UN humanitarian chief Martin Griffiths said. “Casualty figures are rising fast. This is the darkest hour for the people of Ukraine.”

03:01 - Source: CNN
Shock and disbelief brings odd silence as women and children seek refuge in Poland

Foreigners are also desperately trying to leave the country, and some have found themselves waiting in the cold to get out. Others have endured racism from border guards.

Some Ukrainians have opted to stay and join the resistance. Volunteers are pouring into the capital, where there’s a feeling of defiance among many. Some are gathering bottles to make Molotov cocktails.

This story has been updated.

CNN’s Nathan Hodge, Olya Voitoych, Jeremy Herb, Lauren Fox, Ted Barrett, Clare Foran, Kaitlan Collins, Ali Zaslav, Liam Reilly, Pooja Salhotra, Paul P. Murphy, Morgan Rimmer, Richard Roth, Nick Paton Walsh, Oleksandra Ochman, Tim Lister, Stephanie Busari, Nimi Princewill and Shama Nasinde, Arwa Damon, Clarissa Ward, Hannah Ritchie and Teele Rebane contributed to this report.