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.
At least 40 people have been killed Thursday in Russia's attack on Ukraine, according to Oleksiy Arestovich, an adviser to Ukrainian President Volodymyr Zelenskyy.
Arestovich told ABC News that several dozen others have been injured so far.
-ABC News' Patrick Reevell
Russia appears to be establishing military censorship of media coverage of its invasion of neighboring Ukraine.
The Russian Federal Service for Supervision of Communications, Information Technology and Mass Media, or Roskomnadzor, warned Thursday that all Russian media outlets are required to use information exclusively from official Russian sources while covering the military operations in eastern Ukraine.
"Roskomnadzor informs media outlets and information resources that they are required to use information received exclusively from official Russian sources in their materials and reports covering the special operation in the Luhansk and Donetsk people's republics," the agency said in a statement.
Roskomnadzor warned that publishing knowingly false information will result in an administrative fine of up to 5 million rubles (about $60,000).
"The number of unverified and untrue reports published by media outlets and other online information resources has considerably grown in recent hours," the agency added.
-ABC News' Tanya Stukalova
Russia's parliament speaker claimed Thursday that the "sole purpose" of the country's invasion of Ukraine "is to secure peace," saying "Russia has never been an enemy."
"I am calling on Ukrainian citizens: We have always deemed you to be a fraternal people. The sole purpose of what our country is doing is to secure peace," State Duma Speaker Vyacheslav Volodin said in a statement. "We are asking you to step aside and do not take part in any mobilization campaigns proposed by the Kyiv authorities. They are not independent, all orders come from Washington and Brussels."
Volodin also urged Ukrainian Armed Forces to lay down their weapons, saying the orders given from Kyiv are criminal and serve the interests of NATO and the United States. He noted that Russia and Ukraine share history, culture and religion.
-ABC News' Anastasia Bagaeva
Russian forces are attacking Ukraine "from the north, east and south," according to Ukrainian President Volodymyr Zelenskyy.
"Our soldiers are heavily fighting, the aggressor suffered heavy losses," Zelenskyy said in an address to the Ukrainian public from Kyiv on Thursday morning. "We have wounded soldiers."
He added that the Ukrainian military "is giving and will give weapons to everyone who is able to defend out country."
The Ukrainian president also announced that his country has "cut diplomatic ties with Russia."
"Ukraine is defending its freedom," he said. "Citizens of Russia will choose today their own way. Time for you to come out and protest this war with Ukraine."
Just hours before Russia launched the early morning invasion of its ex-Soviet neighbor, a senior Pentagon official told ABC News: "You are likely in the last few hours of peace on the European continent for a long time to come. Be careful."
-ABC News' Julia Drozd and Martha Raddatz
