In a college gym-turned-shelter, Kyrill Nodikov, a Ukrainian poet who has been published in Ukraine and Russia, told ABC News he and his 20-year-old son are ready to enlist in the war.

Nodikov was seeking refuge in a shelter with his wife, their three kids, a dog and a tabby cat.

There are thousands of families struggling with the same dilemma: whether to take their animals, which makes their exodus far more complicated, or leave them behind. Most have stayed loyal to their animals.

When asked what it would be like to take care of her twins and pets by herself, Oksana, Nodikov's wife, started crying.

Sitting on mats on the floor of the gymnasium, the family gathered in a huddle, hugging, holding and comforting Oksana. And then they did the Ukrainian version of a pinky promise: hooking their pinkies and saying, “Peace, friendship, bubble gum."

-ABC News' Matt Gutman, Brandon Baur and Scott Munro

Russia-backed forces have allegedly seized several neighborhoods in Mariupol amid an ongoing operation to " liberate" the southeastern Ukrainian port city.

"The operation to liberate the city of Mariupol of nationalists has been continuing," Russian Ministry of Defense spokesman Igor Konashenkov said at a press briefing. "Donetsk People's Republic militia units have taken control of the neighborhoods of Azovsky, Naidenivka, Lyapyne, and Vynohradar and approached the Azovstal plant. The western neighborhood in the western part of the city has been liberated."

The self-declared Donetsk People's Republic is one of two Russia-controlled separatist areas in eastern Ukraine's Donbas region.

A "small number" of soldiers from the United Kingdom may have "disobeyed orders" by joining Ukraine's fight against invading Russian forces, according to a spokesperson for the British Army.

"We are aware of a small number of individual soldiers who have disobeyed orders and gone absent without leave, and may have travelled to Ukraine in a personal capacity," the British Army spokesperson told ABC News in a statement Wednesday night. "We are actively and strongly encouraging them to return to the U.K."

Personal information on the individuals is not being released for privacy reasons, according to the spokesperson.

The U.K. is advising against all travel to Ukraine and warned that going to fight or assist others engaged in the conflict may be against the law or could lead to prosecution. The U.K., along with its allies, is providing a range of support to Ukraine, including enhancing the country's defense capability. But that support is fundamentally defensive in nature and neither NATO nor Ukraine pose any aggressive threat to Russia, according to a spokesperson for the U.K. Ministry of Defense.

"All Service Personnel are prohibited from travelling to Ukraine until further notice," the U.K. defense ministry spokesperson told ABC News in a statement. "This applies whether the Service Person is on leave or not. Personnel travelling to Ukraine will face disciplinary and administrative consequences."

The spokesperson noted that the U.K. has incredibly limited consular support in Ukraine and is unlikely to be able to offer assistance to any citizens there. There are many ways people can support Ukraine, including through charitable donations, according to the spokesperson, who acknowledged the strong desire to want to help defend freedom and democracy in Europe.

-ABC News' Guy Davies

At least three people, including a child, were killed by a Russian airstrike on a children's hospital and maternity ward in the southeastern port city of Mariupol on Wednesday, according to Ukrainian President Volodymyr Zelenskyy.

Another 17 people, including children, women and health workers, were wounded, Zelenskyy said.

The Ukrainian leader accused Russian state media of lying about the lack of patients inside the hospital at the time of the attack.

"War crimes are impossible without propaganda that covers them," Zelenskyy said in a televised address Thursday. "You will bear responsibility as well as those who give orders to throw bombs on peaceful people."

According to Zelenskyy, 60,000 people managed to evacuate from some areas of Ukraine on Wednesday but Russian forces continue to block Mariupol as well as the small city of Volnovakha.

"Russian troops have already caused a humanitarian catastrophe in Ukraine. But it's just a part of their plan," he said.

Zelenskyy vowed to "rebuild everything" that was destroyed once the war has ended.

"I promise it personally," he added.

European Union leaders are expected to meet in the coming days to discuss Ukraine's application to join the bloc.

"We are waiting for the concrete signal, we are waiting for powerful support because this will be fair, this will be real, this will be human, this will be European," Zelenskyy said. "We know for sure who takes which position in the EU. We know who stands for us and who thinks that the EU is just an accounting department that counts profits, spending and no more."

-ABC News' Yulia Drozd

Ukrainian President Volodymyr Zelenskyy on Wednesday praised the United Nations General Assembly for its vote to condemn the Russian invasion and call for the withdrawal of Russian troops. 

Zelenskyy called the results of the vote "destructive" for the aggressor, and said it shows "a global anti-Putin coalition has been formed and is functioning."

“I praise the approval by the #UN GA with an unprecedented majority of votes of the resolution with a strong demand to Russia to immediately stop the treacherous attack on. I’m grateful to everyone & every state that voted in favor. You have chosen the right side of history," Zelenskyy said in a tweet. 

"The world is with us. The truth is on our side. Victory will be ours!” Zelenskyy said.