Mr Biden said he would use a G7 meeting on Thursday morning to draw up ‘further consequences’ for Russia’s actions.
Russian President Vladimir Putin announced the action during a televised address early on Thursday morning, saying the move was a response to threats from Ukraine.
Mr Biden said in a statement: “The prayers of the entire world are with the people of Ukraine tonight as they suffer an unprovoked and unjustified attack by Russian military forces.
“President Putin has chosen a premeditated war that will bring a catastrophic loss of life and human suffering. Russia alone is responsible for the death and destruction this attack will bring, and the United States and its Allies and partners will respond in a united and decisive way. The world will hold Russia accountable.”
Mr Putin said Russia does not have a goal to occupy Ukraine, but the responsibility for bloodshed lies with the Ukrainian “regime”.
He also warned other countries that any attempt to interfere with the Russian action would lead to “consequences they have never seen”.
Mr Putin accused the US and its allies of ignoring Russia’s demand to prevent Ukraine from joining Nato and offer Moscow security guarantees.
He said the Russian military operation aims to ensure a “demilitarisation” of Ukraine, adding that all Ukrainian servicemen who lay down arms will be able to safely leave the zone of combat.
The Ukrainian Minister of Foreign Affairs, Dmytro Kuleba, said that Ukraine would defend itself against the Russian aggression “and will win”.
“Putin has just launched a full-scale invasion of Ukraine,” he said on Twitter.
“Peaceful Ukrainian cities are under strikes. This is a war of aggression. Ukraine will defend itself and will win. The world can and must stop Putin. The time to act is now.
Foreign Secretary Liz Truss said she “strongly” condemned the “appalling, unprovoked” attack.
She wrote on Twitter: “We stand with Ukraine and we will work with our international partners to respond to this terrible act of aggression.”
A UK Government spokesperson said Russian military action in Ukraine would be “a massive strategic mistake” and would “incur severe costs”.
Mr Putin’s announcement came just after airspace over all of Ukraine was shut down to civilian air traffic, and at the same time as an emergency meeting of the UN Security Council was taking place.
At the end of that meeting, the UK’s ambassador to the UN, Dame Barbara Woodward, said the Russia’s action was “unprovoked and unjustified”.
She said: “It is a grave day for Ukraine and for the principles of the United Nations. As we sat in this chamber urging Russia to step back, President Putin announced special military operations on Ukrainian territory. This is unprovoked and unjustified.
“We and our partners have been clear that there will be consequences for Russia’s actions. We fully support the United States’ call for a UN Security Council resolution. This Council must do all it can to stop war and uphold the (UN) Charter”.
Explosions could be heard in the Ukrainian capital of Kyiv shortly after Mr Putin’s address, while explosions were also reported in the cities of Odesa and Kharkiv.
Nato Secretary General Jens Stoltenberg said Russia’s actions were a “grave breach of international law” and that allies would meet to address the “renewed aggression”.
He said on Twitter: “I strongly condemn #Russia’s reckless attack on #Ukraine, which puts at risk countless civilian lives. This is a grave breach of international law & a serious threat to Euro-Atlantic security. #NATO Allies will meet to address Russia’s renewed aggression.”
Melinda Simmons, the UK’s ambassador to Ukraine, said she was “horrified” at Russia’s action.
She wrote on Twitter: “A wholly unprovoked attack on a peaceful country is unfolding. Horrified. Just because you’ve prepared and thought about this possibility for weeks and months doesn’t mean it isn’t shocking when it actually happens.”
Mr Biden anticipated using Thursday morning’s G7 meeting to draw up “further consequences” for Russia’s action.
He said: “I will meet with my G7 counterparts in the morning and then speak to the American people to announce the further consequences the United States and our allies and partners will impose on Russia for this needless act of aggression against Ukraine and global peace and security.
“We will also coordinate with our Nato allies to ensure a strong, united response that deters any aggression against the alliance. Tonight, Jill and I are praying for the brave and proud people of Ukraine.”
On Wednesday night, Ukrainian President Volodymyr Zelensky made an emotional televised address in Russian following the approval of a 30-day state-of-emergency order, which handed the government sweeping powers in the interest of national security.
“The people of Ukraine and the government of Ukraine want peace. But if we come under attack that threatens our freedom and lives of our people we will fight back,” he said, as he rejected Moscow’s claim Ukraine is a threat to Russia.