U.S. Secretary of State Antony Blinken said Saturday his visit to Poland comes at "one of the most urgent moments in the long history of friendship between our two countries."

Speaking at a joint press conference with Polish Foreign Minister Zbigniew Rau in the southeastern city of Rzeszow, Blinken said the ideals that bind Poland and the United States are "under threat in this region like never before."

"We will stand together, as we've been standing together, in support of Ukraine and against Russia's unprovoked unwarranted premeditated invasion," Blinken told reporters.

Out of the more than 1.36 million people who have been forced to flee Ukraine since Russian forces invaded on Feb. 24, over 756,000 have crossed into neighboring Poland, according to the latest figures from the United Nations High Commissioner for Refugees (UNHCR).

Blinken noted that "at this moment of crisis for millions of Ukrainians and as the security of Europe hangs in the balance," it's an "incredibly powerful reflection of Poland's values that those fleeing the war will find refuge in Poland."

He outlined U.S. funding to support the needs of Ukrainian refugees in Poland and other countries, including a $2.75 billion requested aid package and the $54 million in humanitarian assistance announced last week.

Meanwhile, Rau warned Russia that Poland would not recognize any territorial transfers taken by force. He told reporters that Russian shelling of residential areas and a nuclear power plant in Ukraine "are war crimes under international law" and should "be prosecuted with utmost determination."

The U.S. has yet to say whether Russia has engaged in war crimes in Ukraine.

-ABC News' Justin Gomez

A senior U.S. official told ABC News on Saturday that they have no doubt Russia's indiscriminate bombing of Ukraine will increase in the coming days.

When asked how long they think Ukraine can hold out, the official said Ukrainian forces as a "whole" are degrading but are strong and growing as individuals or "partisans." At least 500 "fighters" from elsewhere crossed into Ukraine on Friday to join the fight against Russia, according to the official.

-ABC News' Martha Raddatz

More than 1.36 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).

More than 756,000 of the refugees from Ukraine are in neighboring Poland, UNHCR figures show.

Russia's flagship airline Aeroflot announced Saturday that it will temporarily suspend all international flights from March 8.

In a statement on its website, the airline cited "the occurrence of additional circumstances that impede the operation of flights."

"The cancellation also applies to international destinations in the schedule of Rossiya and Aurora airlines," Aeroflot said.

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