Gen. Mark A. Milley, the chairman of the Joint Chiefs of Staff, spoke with his military counterparts in France, Poland, Romania and Bulgaria Thursday about the latest developments in Ukraine, according to the Pentagon.

While the Pentagon didn't provide many details about his discussions with the military leaders, it said they shared assessments and intelligence.

Milley also discussed the recent deployment of U.S. military forces to Poland and Romania with their respective military leaders, according to the Pentagon.

-ABC News' Luis Martinez

While tens of thousands of Ukrainians were able to flee the country via humanitarian corridors on Thursday, those still in Mariupol have not been able to leave, as the city is under total siege by Russian forces.

A second attempt for residents to leave on Thursday was abandoned as the Russian military continued to bombard the Mariupol and the humanitarian passages surrounding it, Ukrainian President Volodymyr Zelenskyy said during a press briefing Thursday.

About 300,000 are suffering from lack of water, power and food, said Iryna Vereshchuk, a vice prime minister helping oversee the evacuations. Russia also destroyed and mined surrounding cities, Vereshchuk said.

Albert Khomyak, who lived in Mariupol's eastern outskirts, told ABC News that Russian troops have now entered their street.

"They are trying to destroy Mariupol, that way to destroy the resistance," he said.

Khomyak was somehow able to drive with his family in their own car out of the city, he said.

About 16,000 people are estimated to have evacuated Ukraine on Thursday now that the corridors near the northern Sumy region and some of the towns just northwest of Kyiv have been firmed up, Russian officials said.

But the ceasefires that allow these evacuations are temporary and very imperfect, and sporadic firing still happens throughout them.

The ceasefires then end at 9 p.m., when full-scale offensive attacks from Russia begin again.

-ABC News' Fidel Pavlenko and Natalie Vikhrov

The soaring gas prices Americans are experiencing are a result of the "stand" being taken for democracy in Ukraine, Rep. Raul Ruiz, D-Calif., said in a press conference Thursday from Philadelphia, where a retreat for House Democrats is ongoing.

Ruiz recast rising gas prices in a different light, saying they are part of the fight for democracy and in support of Ukraine against Russia.

"We have to ask ourselves, what is it we stand for as a democracy?" Ruiz, the chair of the Congressional Hispanic Caucus, said. "To protect other democracies, and to protect us from autocracies and to show solidarity? What is the price that we as individuals will want to contribute in solidarity with the Ukrainian people?"

Ruiz said his family are among the millions of Americans feeling the effects of the record-high prices.

"I, for one, am going to pay that price," Ruiz said. "If it means paying a few extra cents at the gas tank, then we're willing to pay that."

-ABC News' Ben Siegel

A senior U.S. defense official said Thursday that the U.S. has seen "indications" of Russia using a potential false flag operation about U.S.-Ukrainian biochemical weapons development as a pretext for the potential use of "these kinds of agents in an attack."

"We have picked up indications that the Russians could be making these claims, these false claims, about us and Ukrainian work in bio-defense, as a way of creating a pretext of their own to perhaps use these kinds of agents in an attack,” said the official.

On Thursday, there was a united front from the White House, State Department and the Pentagon rejecting Russian claims that the U.S. and Ukraine are developing these weapons, noting that Russia has previously used false flags and claims to justify the use of the very weapons they’ve made claims about.

When asked what prompted the U.S. to go public again with intelligence about a potential Russian false flag operation, a senior U.S. defense official would only describe "indications" of potential use.

"We're doing this because the Russians and the Chinese felt somehow important for them to put out a bunch of lies. They just flat out lied,” said the official. “We believe that this is potentially some sort of pre-textual argument that they are creating. We have indications of that."

The official added, “I won't get into how long we've had these indications or what the sources are thinking can understand that. But we believe their public narrative could be used, being used as a way to create that, that pretext."

When asked if that meant the U.S. had seen the movement of chemical or bio weapons near Ukraine or into Ukraine the official stuck to "indications". “I have to leave it with you with indications and [I’m] not going to be at liberty to go in more detail than that today.”

A senior defense intelligence official added that the U.S. assesses that Russia maintained an offensive bio-weapons program in violation of current conventions and no issues have been noted about Ukraine.

Ukraine’s intelligence agency also warned on Thursday that there are signs Russia might be planning to blow up a huge ammonia stockpile in eastern Ukraine as a false flag.

-ABC News' Luis Martinez

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