CNN  — 

Ukrainians face an increasingly desperate situation on the ground as Russian forces hit the capital and fresh targets across the country, despite both nations acknowledging signs of progress in ongoing negotiations.

A theater where hundreds of people had taken shelter in the besieged southern city of Mariupol was bombed on Wednesday, according to local authorities, as hundreds of thousands of people remain trapped in the coastal Ukrainian city that has been encircled for weeks by Russian forces.

The word “children” was spelled out on two sides of the theater before it was struck, according to satellite images.

Northern cities have come under increased attack, including the capital Kyiv, with two people injured in the shelling of a 12-story residential building early Wednesday.

In the nearby Ukrainian city of Chernihiv, at least 10 people queueing for bread were killed when Russian forces shelled it on Wednesday, a local official, Vyacheslav Chaus, told Ukrainian television. He said the attack was indicative of Russia’s use of indirect fire against civilians.

Despite this, Russian forces are still “generally stalled” near Kyiv, and have not “made any significant advances” towards the city from the north, northwest or east of the city, a senior US defense official told reporters Wednesday.

As the Russian assault intensifies, Ukrainian President Volodymyr Zelensky said Wednesday that Russia’s negotiating position in talks between the two countries was becoming “more realistic,” a sentiment reiterated by Russia’s Foreign Minister Sergey Lavrov, who suggested there was “a certain hope for reaching a compromise,” in a televised interview to Russian media outlet RBK.

But while the United States welcomes “the sentiments expressed that there is hope, that there is optimism for diplomatic progress,” it believes Russia must de-escalate for any such progress to actually be achieved, US State Department spokesperson Ned Price said Wednesday.

Deteriorating situation in ‘hell’ of Mariupol

Russian military strikes continue to bombard Mariupol, which has been besieged by Russian forces since the beginning of March.

Petro Andruishchenko, an adviser to the mayor of Mariupol, described the bombed theater as the largest shelter “in number and size” in the city’s center. “According to preliminary data, more than a thousand people were hiding there,” he said. “The probability of getting there to dismantle the rubble is low due to constant shelling and bombing of the city.”

The bombing adds to the city’s growing humanitarian crisis. About 350,000 people are trapped in the city and as many as 2,500 civilians have died, Ukrainian officials estimate. Those who remain are without electricity, water and heat.

A woman walks past building damaged by shelling in Mariupol on Sunday.

Satellite images from Maxar Technologies Monday showed the extent of the damage in Mariupol, including homes smoldering after apparently suffering Russian strikes, a destroyed apartment complex and rising plumes of thick smoke.

After weeks of failed attempts to establish safe civilian evacuation corridors, about 20,000 people managed to leave the city on Tuesday, officials say. And on Wednesday, more than 3,000 cars transporting evacuees from Mariupol arrived in the central Ukrainian city of Zaporizhzhia, the head of the regional administration, Oleksandr Starukh, said on his Telegram channel.

However, Russian forces also attacked Zaporizhzhia for the first time on Wednesday, hitting a railway station and the area around the botanical garden, Starukh added.

A man looks at a burned apartment building that was damaged by shelling in Mariupol on Sunday.

In another southern coastal city, the Ukrainian government said it staged a rescue of the mayor of Russian-occupied Melitopol, who was detained by armed men in the city on March 11.

Melitopol Mayor Ivan Fedorov was freed as part of a prisoner swap, Ukraine’s Center for Strategic Communications and Information Security said in a statement on Wednesday.

According to the statement, Fedorov was exchanged for nine Russian soldiers, which the Ukrainians say are “conscripts,” born between 2002-2003. Russia has denied sending conscripts to Ukraine.

Since Fedorov’s detention, newly installed mayor Galina Danilchenko ordered the broadcasting of Russian television channels and attempted to dissolve the city council and instead create a People’s Committee.

Later Wednesday, a senior advisor to Zelensky said the Ukrainian army is beginning to counterstrike Russian forces in a number of directions.

“This fact is drastically changing the dispositions of the sides,” Mykhailo Podolyak said in a statement posted to Telegram, adding that the “Russian administration is trying to find allies whose soldiers would be ready to die on the field.”

NATO ‘not as essential’

Amid signs of potential progress in Ukrainian-Russian talks, the Kremlin said Wednesday that President Vladimir Putin hadn’t spoken to his US counterpart, Joe Biden, since the beginning of the war in Ukraine, but contact between the two leaders can resume if necessary.

Vladimir Medinsky, the head of the Russian negotiating delegation, was quoted Wednesday as saying the talks were “difficult” and “slow,” and that Moscow’s objectives in negotiations with Ukraine have not changed.

Russian Foreign Minister Sergei Lavrov said there was hope of a compromise in negotiations with Ukraine.

Medinsky was quoted by state media RIA Novosti on Wednesday as saying Moscow wants a “peaceful, free, independent and neutral” Ukraine. He added that the country should not be a member of NATO or any military bloc.

Putin sees NATO’s expansion as an existential threat, and the prospect of Ukraine joining the Western military alliance a “hostile act. This week, Zelensky appeared to shift away from his previous demand for NATO membership for Ukraine

The Ukrainian President delivered an impassioned speech to members of Congress on Wednesday via videolink, receiving a bipartisan standing ovation both before and after his statement.

Showing a graphic video of Russia’s attacks on Ukraine, Zelensky repeated his calls for a no-fly zone in Ukraine and made references to Mount Rushmore, the attacks on Pearl Harbor and the terrorist attacks of September 11, 2001.

Ukrainian President Volodomyr Zelensky urged his US counterpart Joe Biden to be "the leader of peace."

“In the darkest time for our country, for the whole Europe, I call on you to do more,” Zelensky said. “New packages of sanctions are needed, constantly, every week until the Russian military machine stops. Restrictions are needed for everyone on whom this unjust regime is based.”

Olha Stefanishyna, deputy prime minister for European and Euro-Atlantic Integration of Ukraine, told CNN the reason why Zelensky did not mention NATO is because it is “not as essential” as a no-fly zone and weapons – and that political aspirations will have to go on hold for now.

“I think that NATO is something which is not as essential as a no-fly zone and more weapons and basically, capability to defend ourselves,” she told CNN from a secure location in Kyiv.

“But now basically it’s not about politics, it’s about survival,” she added.

Stefanishyna said Putin is failing in the war because “the chain of command which disinforms him, and the senior management around, shows that they know nothing about our nation.”

“I’m absolutely sure that he’s uncomfortable in every moment that he’s sitting in his bomb shelter,” she said, adding, “he fails in each of his assessments.”

While US officials say the White House does not support instituting a no-fly zone over Ukraine or supplying the Ukrainian Air Force with new fighter aircraft, Biden appeared to shift his stance on Putin.

“I think he is a war criminal,” Biden said to reporters after remarks at the White House on Wednesday. He and other government officials had previously stopped short of saying war crimes were being committed in Ukraine, citing ongoing investigations into whether that term could be used.

CNN’s Tim Lister, Oleksandra Ochman, Vasco Cotovio, Sam Kiley, Kostan Nechyporenko and Gianluca Mezzofiore contributed to this report.