Ukrainian President Volodymyr Zelenskyy issued a warning to his Russian President Vladimir Putin on Thursday, as Russian forces continued their offensive.

"You will repay everything you did against Ukraine -- in full," Zelenskyy said in a televised statement. "And we will not forget those who perished -- and God won't."

Zelenskyy noted that his country receives "more and more powerful weapons everyday" from "partners" and "real friends." He also likened the Russian invasion to being "attacked by another virus."

"Exactly two years ago, the first case of COVID-19 was recorded in Ukraine. The first weeks of fighting it were extremely difficult, but we were united and therefore strong and therefore we withstood," he said. "Exactly a week ago, Ukraine was attacked by another virus, another disease, by those who suffer from severe annexation and occupation of foreign lands. The first hours and days of full-scale war were extremely difficult, but we were united and therefore strong and therefore we withstood. And it will be so and we will continue to stand."

Russia's state space corporation Roscosmos announced Thursday its decision to suspend supplies of Russian-made rocket engines to the United States.

"In this situation, we can no longer supply the U.S. with our rocket engines that are the best in the world," Roscosmos CEO Dmitry Rogozin said on state-owned television channel Russia-24. "Let them fly on something else, like their brooms or whatever. But at least we are freezing our shipments."

-ABC News' Tanya Stukalova

Russian forces continue to intensely bombard the key Ukrainian port city of Mariupol, according to local councillor Petro Andrushenko.

Speaking to ABC News by telephone from a bomb shelter in Mariupol on Thursday, Andrushenko said Russian forces have been striking the southern city with missiles and heavy artillery non-stop for more than 24 hours. He said the firing was continuing even as he spoke, hitting the city center.

Mariupol is now besieged and surrounded by Russian troops. A last column of journalists and diplomats managed to pull out on Wednesday under the guns of advancing Russian forces.

Andrushenko said one neighborhood, Livoberezhna, has been "destroyed" and that authorities have tried to evacuate the residents there. The entire city is without power and has waning supplies, according to Andrushenko.

"We haven't any heat, we haven't any water, we haven't any electricity, but we have Russian rockets," he told ABC News.

At least 10 people have been killed and 150 others have been injured in Mariupol so far, according to Andrushenko. But it's virtually impossible to get an accurate count because authorities are unable to recover bodies under such heavy bombardment.

Andrushenko said he believes Russia is trying to make Mariupol "like Aleppo," the Syrian city that the Russian military helped Syrian government forces devastate during a siege there in 2016. Aleppo ultimately became a symbol of the brutality of the Syrian civil war.

“They want to do like Aleppo for Mariupol now," Andrushenko said, "because Mariupol is a symbol of Ukrainian power."

-ABC News' Patrick Reevell

More than 1 million people have been forced to flee Ukraine since Russian forces invaded on Feb. 24, according to the latest figures from the United Nations High Commissioner for Refugees (UNHCR).

Over 50% of the refugees from Ukraine are in neighboring Poland, UNHCR figures show.

"In just seven days, 1 million people have fled Ukraine, uprooted by this senseless war," U.N. High Commissioner for Refugees Filippo Grandi said in a statement Thursday. "I have worked in refugee emergencies for almost 40 years and rarely have I seen an exodus as rapid as this one."

"Hour by hour, minute by minute, more people are fleeing the terrifying reality of violence. Countless have been displaced inside the country," he added. "Peace is the only way to halt this tragedy."

-ABC News' Zoe Magee

While Poland has been welcoming refugees fleeing the destruction in Ukraine, the country will eventually meet its limit on how many people it can take in, Konrad Fijolek, president of Rzeszow, Poland, a city about 60 miles from the Ukrainian border, told ABC News.

Like many cities that border Ukraine, Rzeszow, a town of about 180,000 people, has become a pathway to safety and a lifeline for millions of refugees flooding across the border from Ukraine.

Poland will be able to receive about 1.5 million people, but any more will put the country under strain, Fijolek said.

"If a million or more come, we won't be able to cope," he said.

Some estimates suggest as many as 4 million people could leave Ukraine due to the conflict, but most of the major cities in the country are already full — and officials are attempting to move refugees into smaller cities, a feat that is "not easy," Fijolek said.

So far, all the shelters set up in Poland are temporary, he added.

"We would like to avoid the view of refugee camps here," he said. "We would like people who are escaping from the war to think that what awaits here is proper camp not camps."

In addition, the mental state among the people in Poland is continuing to deteriorate, Fijolek said.

"We as local leaders would like to send the message that if there's any possible action to stop the war [find it] and then try to negotiate, because every day at the border we can see the human tragedy," he said.

-ABC News' Chris Donato and Marcus Moore