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.
The U.S. administration has urged Ukrainian President Volodymyr Zelenskyy to head to Lviv, in the western part of the country, for his safety, a U.S. official told ABC News.
-ABC News’ Chief Global Affairs Correspondent Martha Raddatz
President Joe Biden spoke with French President Emmanuel Macron and German Chancellor Olaf Scholz on Monday afternoon, in which all three leaders "strongly condemned" Russian President Vladimir Putin’s decision to recognize separatist regions in Ukraine as independent, the White House announced in a statement.
"The leaders strongly condemned President Putin’s decision to recognize the so-called DNR and LNR regions of Ukraine as 'independent,'" the statement read. "They discussed how they will continue to coordinate their response on next steps."
NATO Secretary General Jens Stoltenberg also condemned Putin’s decision, stating, "This further undermines Ukraine’s sovereignty and territorial integrity, erodes efforts towards a resolution of the conflict, and violates the Minsk Agreements, to which Russia is a party."
-ABC News' Patrick Reevell and Christine Theodorou
In the decree signed by Russian President Vladimir Putin recognizing independence for two Russian-controlled separatist regions in eastern Ukraine's Donbas region, Putin ordered Russia's Defense Ministry to assist the separatist forces in "maintaining peace."
This degree gives Russia's military a basis to openly enter the regions.
The decree specifies that Russia's forces should maintain the "peace" before the formal signing of a treaty of "friendship, cooperation and mutual aid" between Russian and the "republics."
The decree also orders Russia's foreign ministry to begin establishing diplomatic relations with the two separatist "republics."
"In connection with the appeal of the head of the Donetsk's People's Republic, the Ministry of Defense of the Russian Federation is to ensure before the conclusion of the agreement, named in point three of the present Decree, the fulfilment by the Armed Forces of the Russian Federation on the territory of the People's Republic of Donetsk the function of maintaining the peace," the decree reads.
-ABC News' Patrick Reevell
French President Emmanuel Macron is calling for an emergency United Nations Security Council meeting and "targeted European sanctions" in the wake of Russian President Vladimir Putin announcing recognition of independence of two Russian-controlled separatist regions in eastern Ukraine's Donbas region.
"This is clearly a unilateral violation of Russia's international commitments and an attack on Ukraine's sovereignty," the Elysée Palace said.
United Nations Secretary-General António Guterres is "greatly concerned" by Putin's decision, which he considers to be a violation of Ukraine's territorial integrity and sovereignty, a spokesperson said.
"The United Nations, in line with the relevant General Assembly resolutions, remains fully supportive of the sovereignty, independence and territorial integrity of Ukraine, within its internationally recognized borders," the spokesperson said. "The Secretary-General urges all relevant actors to focus their efforts on ensuring an immediate cessation of hostilities, protection of civilians and civilian infrastructure, preventing any actions and statements that may further escalate the dangerous situation in and around Ukraine and prioritizing diplomacy to address all issues peacefully."
Ukrainian Foreign Minister Dmytro Kuleba had called for a U.N. Security Council meeting earlier in the day. The U.S. is now backing the call, with Ambassador Linda Thomas-Greenfield saying in a statement that the U.N.’s highest body "must demand that Russia respect the sovereignty and territorial integrity of Ukraine, a UN Member State."
"We must all stand with Ukraine in the face of this brazen attempt to usurp Ukraine's sovereign territory," Thomas-Greenfield said. "There can be no fence-sitters in this crisis."
