AVDIIVKA, UKRAINE - OCTOBER 26: Two Ukrainian soldiers walk along the destroyed city in the fog on October 26, 2023 in Avdiivka, Ukraine. Fighting has intensified in recent days after Russia launched a major offensive here earlier this month. (Vlada Liberova / Libkos via Getty Images)
Kyiv CNN  — 

This week, Ukrainian forces continued to hold out against a renewed offensive in eastern Ukraine as the White House claimed Russia is executing its own troops for disobeying orders.

In southern Ukraine, authorities issued evacuation orders for civilians where Russia has stepped up aerial attacks.

Strikes in a western Ukrainian city blew out windows at a nuclear power plant, once again raising safety concerns.

Here are the key developments…

Executing its own

The US says Russia is executing its own soldiers and has threatened entire units with execution for failing to obey orders.

National Security Council coordinator for strategic communications John Kirby told reporters: “We have information that the Russian military has been actually executing soldiers who refuse to follow orders, we also have information that Russian commanders are threatening to execute entire units if they seek to retreat from Ukrainian artillery fire.”

Kirby did not provide further details on the claim that Russia was executing its own. Russia has previously been accused of using “barrier troops” to keep soldiers from deserting the front lines.

“It’s reprehensible to think about – that you would execute your own soldiers, because they didn’t want to follow orders, and now threatening to execute entire units is barbaric,” he said.

Russia’s mobilized forces in the region “remain under-trained, under-equipped and unprepared for combat,” Kirby said, and have been largely used in what he called “human wave tactics” as it attempts to forge ahead with a renewed offensive.

While Russia continues to have some offensive capability and may achieve some tactical gains on the battlefield, it continues to show no regard for the lives of soldiers,” Kirby told reporters.

AVDIIVKA, UKRAINE - OCTOBER 26: An elderly civilian woman stands with a cat on the balcony of her destroyed house in the city of Avdiivka on October 26, 2023 in Avdiivka, Ukraine. She used to be a Ukrainian language teacher before the full scale invasion. Fighting has intensified in recent days after Russia launched a major offensive here earlier this month. (Vlada Liberova / Libkos via Getty Images)

Tough battles in Avdiivka and Kupiansk

Russia continues its brutal offensive in eastern Ukraine.

In the city of Avdiivka, Ukraine claimed it had been successful in repelling assaults and taking out large numbers of Russian soldiers.

Rain over the last few days has slowed down Russian forces as they continue efforts to encircle the city and take over high ground. “Moving on foot on wet ground is difficult, let alone moving heavy equipment,” a local military official said.

“Our warriors stopped them and inflicted heavy losses on the enemy, who lost at least a brigade of personnel,” Ukrainian President Volodymyr Zelensky said.

CNN cannot independently verify Ukrainian claims of Russian losses, but videos from the battlefield shared by unofficial Ukrainian military accounts show intense fighting and destroyed hardware.

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Avdiivka has been a front line city since 2014, when Moscow-backed separatists seized a large portion of the Donbas region. It has been under fire since Russia launched its full-scale invasion in February 2022. Most residents have fled the fighting. Some of the remaining civilians are trickling out of the city with the help of the police.

In Kupiansk, Ukrainian soldiers are fighting off Russian efforts to capture a strategic railway interchange.

Assaults are around the clock, according to Ukrainian military on the ground.

Kupiansk was occupied by Russian forces for nearly seven months early on in the war. Since its liberation in September 2022, the Ukrainian military has been trying to resist Russian assaults. The city is strategically important