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.
Ukraine's Ministry of Internal Affairs released an update on the number of civilians who have been killed or wounded.
As of Sunday evening, 352 people have been killed, including 14 children, according to the agency.
There are 1,684 wounded civilians, 116 of which are children.
-ABC News' Christine Theodorou
The United Nations Security Council voted to convene a special session of the U.N. General Assembly to debate Russia's invasion of Ukraine.
Eleven nations voted in favor of the session, while Russia voted against it. India, China and the United Arab Emirates abstained.
This will mark the eleventh time since 1950 that the General Assembly convened an emergency session.
"The special session is a necessary new step intended to defend the U.N. Charter and international law and put an end to the aggressions against Ukraine. In parallel, the Security Council will of course continue to assume its primary responsibility for the maintenance of international peace and security," Nicolas de Rivière, the permanent representative of France to the U.N., said before the vote.
-ABC News' Christine Theodorou
The U.S. embassy in Moscow sent an alert urging American citizens to consider departing Russia immediately amid the growing number of canceled flights and closures of airspace to Russian airlines.
"U.S. citizens should consider departing Russia immediately via commercial options still available," the alert said.
-ABC News' Conor Finnegan
New York Gov. Kathy Hochul announced an executive order Sunday that ordered a review of all state purchases and investments with Russia and ceased investments for as long as U.S. sanctions are imposed on the country.
“The state will not permit its own investment activity, whether directly or indirectly to aid Russia as it commits these human rights violations,” Hochul said during a news conference.
She also reiterated that refugees from the conflict will be welcome in New York.
“Because we have the Statue of Liberty in our harbor, this is a point of pride for us to welcome all of them,” Hochul said.
