Over 5 million people have now fled Ukraine, according to the United Nations High Commissioner for Refugees.

The majority of those refugees -- over 2.8 million -- are in Poland.

Russia’s military issued another ultimatum on Wednesday, calling for Ukrainian forces to lay down their arms and leave a Mariupol steel plant, according to Russian state media.

Moscow claimed that Ukrainian troops and civilians would be allowed to leave the Azovstal Iron and Steel Works plant without harm during a cease-fire beginning at 2 p.m. local time.

Ukrainian forces at the besieged plant rejected a similar offer on Tuesday.

More than 1,000 civilians are sheltering on the grounds of the sprawling industrial plant, the Mariupol City Council said on Monday.

A Russian official, Dmitry Polyansky, on Tuesday accused Ukrainian troops of using civilians at the plant as human shields.

“One month into the siege of Azovstal plant, those same radicals and neo-Nazis suddenly declared that allegedly there had been civilians inside the plant all that time, even though until yesterday, they had never uttered a word about it," Polyansky told the U.N. Security Council during a session on Ukraine on Tuesday.

As Ukrainian forces brace for a full-scale assault in the eastern part of the country, a U.S. official said the increased pace of operations from Russian forces in the past 24 hours could be probing attacks or the beginning of the main battle for the Donbas.

The defense official said the Russian offensive to seize southeastern Ukraine will likely involve a frontal assault from inside Russia and a double envelopment, or encircling, of Ukrainian forces in the Donbas. Russian forces will come south from Izyum and troops in the Berdyansk area will move north to encircle Ukrainian forces in the Joint Forces Operations area in the Donbas.

But the U.S. defense official said Ukraine has the advantage in the region since they have prepared a defense for years, including digging trenches, preparing anti-armor traps and ambush locations and more.

The U.S. and other countries have now provided close to 70,000 anti-tank weapons to Ukraine as well as 30,000 anti-aircraft missiles and 7,000 launchers to fire them, according to the defense official.

As for stopping the shipments of those weapons, the U.S. believes Russia will target the paths and roads in western Ukraine being used to ship Western military aid into Ukraine even though it has not done so yet. Still, it's believed with the amount of weaponry being delivered to Ukrainian forces, it will be impossible to stop it all.

-ABC News' Luis Martinez

Capitol Hill sources and a Biden administration official confirmed to ABC News that the White House has briefed them on plans to announce another weapons delivery to Ukraine as soon as this week.

The aid could range in the hundreds of millions of dollars and be similar in size to the $800 million package President Joe Biden announced last week, sources familiar with the details said.

Details of the weapons package are still being discussed and could change, a source said.

When asked earlier Tuesday if he plans to send more artillery to Ukraine, Biden told reporters, "Yes."

-ABC News' Mariam Khan and Katherine Faulders

Mariupol has not yet fallen, despite Russia's demands that Ukrainian troops defending the besieged Ukrainian port city surrender, according to Ukrainian Prime Minister Denys Shmyhal.

"There [are] still our military forces, our soldiers, so they will fight until the end," Shmyhal told ABC News' George Stephanopoulos in an exclusive interview Sunday on "This Week."

Mariupol is a strategic city for Moscow because it would allow Russian forces in the south to connect with troops in eastern Ukraine's contested Donbas region. It would also give Moscow a key port.

Although Mariupol remains under the Ukrainian government's control, Shmyhal said the city's residents are suffering.

"They have no water, no food, no heat, no electricity," he said. "They ask all of our partners to support and help stop this humanitarian catastrophe."

-ABC News' Monica Dunn