Biden will announce the news in his State of the Union address, a source said.
Russian forces are continuing their attempted push through Ukraine from multiple directions, while Ukrainians, led by President Volodymr Zelenskyy, are putting up "stiff resistance," according to U.S. officials.
The attack began Feb. 24 as Russian President Vladimir Putin announced a "special military operation."
Russians moving from Belarus towards Ukraine's capital, Kyiv, don't appear to have advanced closer towards the city since coming within about 20 miles, although smaller advanced groups have been fighting gun battles with Ukrainian forces inside the capital since at least Friday.
Russia has been met by sanctions from the U.S., Canada and countries throughout Europe, targeting Russia's economy and Putin himself.
A spokesperson for the U.N. High Commissioner for Human Rights said 136 civilians have been killed in Ukraine, including 13 children.
Another 400 Ukrainian civilians have been wounded, spokesperson Liz Throssell said.
The 31 countries on the International Energy Agency's Governing Board have agreed to release 60 million barrels of oil from their 1.5 billion barrels of emergency reserves "to send a unified and strong message to global oil markets that there will be no shortfall in supplies as a result of Russia’s invasion," the IEA said in a statement.
Half of this release -- 30 million barrels -- will come from the U.S. strategic reserve, White House press secretary Jen Psaki said.
Russia is the biggest oil exporter on the globe and the third-largest producer, the IEA said.
Filippo Grandi, the United Nations High Commissioner for Refugees, said the number of Ukrainians who've fled their country has climbed to 677,000.
Diplomats from Western countries were seen on video walking out in protest as Russian Foreign Minister Sergei Lavrov addressed the U.N. Human Rights Council and Conference on Disarmament.
The meeting was held Tuesday in Geneva and Lavrov gave his address via video.
The Human Rights Council has faced criticism for years for including human rights abusers, including Russia. In a prerecorded video to the council, Secretary of State Antony Blinken questioned whether Russia should be allowed to keep its seat.
"One can reasonably ask whether a U.N. member state that tries to take over another U.N. member state -- while committing horrific human rights abuses and causing massive humanitarian suffering -- should be allowed to remain on this council," he said.
Blinken accused Russia of hitting civilian targets like schools, hospitals, residential buildings, critical infrastructure, and cars, buses, and ambulances -- including the "monstrous rocket strikes" on an apartment complex in Kharkiv.
"Reports of Russia's human rights abuses and violations of international humanitarian law mount by the hour," he said.
"These are the human rights abuses this council was created to stop. If we cannot come together now, when will we come together?" he asked.
-ABC News' Fergal Gallagher, Conor Finnegan
