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

U.S. Secretary of State Antony Blinken crossed the border into Ukraine Saturday after meeting with Ukrainian Foreign Minister Dmytro Kuleba at the Korczowa Border Crossing Point.

"The entire world stand with Ukraine," Blinken said, and Kuleba added that he hopes Ukrainians will see this as a "clear manifestation that we have friends who literally stand by us."

Blinken said the sanctions imposed so far against Russia are "producing very, very concrete results" and that the pressure will "grow" until this "war of choice is brought to an end."

When asked directly about helping Kuleba with more firepower, Blinken said, "the support for Ukraine not only has been unprecedented, not only is going to continue, it's going to increase."

Kuleba said Ukraine "appreciates" sanctions that have been announced in the last week, but that more economic and political pressure and "necessary weapons," would "save many lives in Ukraine... many sufferings will be avoided."

Kuleba also said that they are “satisfied" with already arranged supplies of anti-tank weapons and ammunition, but that “it’s no secret” they still want fighter jets and air defense systems.

He also thanked the U.S. for sending stingers, and said they were used on Saturday.

"Just today we shot down three Russian attack aircrafts, which were bombing our cities with the use of stingers but we need -- so to say -- big air defense systems to ensure the safety of our skies. If we lose the skies, there will be much, much more blood on the ground,"Kuleba said.

In response to questions about NATO’s refusal to impose a no-fly zone over Ukraine, Kuleba said it’s a "sign of weakness," but stayed optimistic that they will change their minds.

"The time will come," he said.

-ABC News' Conor Finnegan and Justin Gomez