Russia-Ukraine updates: US sanctions Russian military shipbuilder, diamond miner

More than 3.4 million people have fled Ukraine since Russia invaded, according to the latest figures from the United Nations High Commissioner for Refugees.

Monday's update showed that, of those refugees, more than 2 million have crossed the border into Poland. Additionally, about 535,000 have entered Romania and 365,000 have crossed into Moldova.

Refugees are also going to Hungary, Slovakia, Russia and Belarus.

UNHCR chief Filippo Grandi tweeted Sunday that since the Russian invasion, 10 million people in Ukraine fled, either displaced in the country or as refugees abroad.

"Among the responsibilities of those who wage war, everywhere in the world, is the suffering inflicted on civilians who are forced to flee their homes," he wrote.

UNICEF told ABC News that half of the internally displaced Ukrainians and half of those who have fled are children.

-ABC News' Zoe Magee

Ukrainian officials rejected Russia’s demand that they surrender the southern port city of Mariupol on Monday morning.

“There can be no talk of any surrender, laying down of arms," Deputy Prime Minister Irina Vereshchuk said, according to The Associated Press.

Officials instead called on Russia to allow residents to evacuate safely from the city.

President Volodymyr Zelenskyy in an early morning video address said his government was preparing to send buses to Mariupol on Monday to continue the evacuation.

“In besieged Mariupol, Russian aircraft dropped a bomb on an art school. People were hiding there. Hiding from shelling, from bombing,” Zelenskyy said, according to an official translation from his office. “There were no military positions. There were about four hundred civilians. Mostly women and children, the elderly. They are under the debris. We do not know how many are alive at the moment.”

Some who’ve left Mariupol have described dire circumstances, with constant shelling and little access to essentials, including food, water, and medicine, according to a report published Monday by Human Rights Watch.

“Mariupol residents have described a freezing hellscape riddled with dead bodies and destroyed buildings,” Belkis Wille, senior crisis and conflict researcher at Human Rights Watch, said in a statement. “And these are the lucky ones who were able to escape, leaving behind thousands who are cut off from the world in the besieged city.”

In addition to his trip to Brussels, President Joe Biden will also travel to Warsaw, Poland, on Friday, where he will hold a bilateral meeting with President Andrzej Duda.

"The President will discuss how the United States, alongside our Allies and partners, is responding to the humanitarian and human rights crisis that Russia’s unjustified and unprovoked war on Ukraine has created," White House Press Secretary Jen Psaki said in a statement Sunday.

Psaki's statement did not specify if Biden will do anything else during his trip to Poland, which has taken in more than 2 million Ukrainian refugees since the start of the conflict with Russia.

-ABC News' Molly Nagle

Russia has given Ukrainian forces in the besieged city of Mariupol until Monday at 4 a.m. local time to surrender, according to reports.

Gen. Col. Mikhail Mizintsev, a senior Russian commander, warned the city’s local authorities, including the mayor, that if they do not surrender they will face a “military tribunal,” according to Russian state media.

He called on the official authorities in Kyiv to “see reason” and to cancel orders given earlier that he said oblige Ukrainian fighters “to sacrifice themselves and to become the ’martyrs of Mariupol.’”

Russian forces have been trying to push deep into Mariupol, engaging in street-to-street fighting while indiscriminately bombarding the city. Ukrainian troops defending the city are believed to be under severe pressure right now.

Mizintsev said Russia has proposed opening humanitarian corridors beginning at 9 a.m. Monday to allow Ukrainian troops and civilians to leave Mariupol.

He claims Russia’s goals in the city are “purely humanitarian” and repeated Russia’s false claims that it was Ukrainian “nationalist” forces that have destroyed several major civilian buildings, which in reality have been struck directly by Russian air and missile strikes.

“We call on the units of the Ukrainian armed forces, the battalions of the Territorial Defense, foreign mercenaries, to cease military action, lay down their arms and to leave for the territories controlled by Kyiv via the humanitarian corridors agreed with the Ukrainian side,” Mizintsev reportedly said. “Moreover, the safe exit of all those laying down their arms is guaranteed and the sparing of their lives.”