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.

The Russian forces charging toward Kyiv haven't made progress in the last day as they face Ukrainian resistance and low food and gas supply, a senior U.S. defense official told reporters Tuesday.

However, it could be a deliberate pause, the official said. "Part of the stall could be ... as a result of their own self-determined sort of pause in operations -- that they are possibly regrouping, rethinking, reevaluating," the official said.

The U.S. believes Russian forces "have committed now more than 80% of what was their pre-staged combat power," the official added.

The official said some Russian soldiers weren't told they were going into combat. The official said "not all of them were apparently fully trained and prepared."

The strong Ukrainian resistance has also hurt morale, according to the official.

Russia has now launched more than 400 missiles on Ukraine, the official said. The U.S. believes Russia has launchers that could be used for thermobaric weapons, but cannot confirm their use, the official said.

Russian forces are making the most progress in the south. Russians are attacking Kherson in south Ukraine, which "appears very much to be contested city at this point," the official said.

Russians are also approaching Mariupol in southeastern Ukraine, and while they haven't yet entered the city, "they are close enough now that they could attack Mariupol with long range fires," the official said.

Two towns on the path to Mariupol are believed to be occupied by the Russians, according to the official.

The U.S. believes the Russians hope to move north out of Mariupol up to the heavily-contested city of Kharkiv. The official said they believe Russian forces are trying to encircle Kharkiv.

The U.S. official noted that they've seen "certain risk-averse behavior by the Russian military" over the last week.

"Take the amphibious assault, for instance. They put those troops ashore a good 70 kilometers away from Mariupol because they knew Mariupol was going to be defended and they could put them ashore in an uncontested environment. And they still haven't reached Mariupol," the official said.

"They are not necessarily willing to take high risks with their own aircraft and their own pilots," the official said.

"And of course we're seeing that on the ground -- the fairly slow and steady progress that they have made, and you guys are seeing it for yourselves on the ground where ... units are surrendering, sometimes without a fight."

-ABC News' Matt Seyler