Russia has been widely condemned after bombarding cities across Ukraine, including launching missile strikes on the centre of Kyiv for the first time, BBC reported.
The US said the "brutal" attacks had hit non-military targets, including a university and children's playground, and promised ongoing military aid.
United Nations chief Antonio Guterres said he was "deeply shocked".
Vladimir Putin said the attacks were retaliation for Saturday's explosion on a key bridge linking Russia to Crimea.
Ukraine says 83 missiles were launched of which more than 43 were shot down.
In a defiant video, Ukraine's President Volodymyr Zelensky said that "Ukraine cannot be intimidated. It can only be more united."
The deadly barrage included strikes on the cities of Lviv, Kharkiv, Dnipro and Zaporizhzhia, and were some of the worst Ukraine has seen for months.
At least 14 people were killed and scores more were injured, officials said.
Several regions were left without electricity and water after missiles hit energy infrastructure.
Residents in the capital Kyiv said Russia appeared to be targeting civilian areas which were busy with Monday morning commuters, including the children's playground, university and the popular Taras Shevchenko park.
Antonio Guterres described the strikes as "another unacceptable escalation of the war" for which civilians were paying the highest price.
The EU said a war crime had been committed, while European Commission president Ursula von der Leyen said Russia stood for terror and brutality, according to BBC.
Mr Biden said the attacks demonstrated "the utter brutality" of Putin's "illegal war".
China and India, which have not condemned the war, called for a de-escalation.
Speaking at the UN General Assembly in New York, Sergiy Kyslytsya, Ukraine's Ambassador to the UN, said his family had been in a residential area in Ukraine when it was attacked by the latest Russian missiles and they were unable to go to a bomb shelter.
He said Russia had already killed some of his relatives, calling it "a terrorist state" that must be deterred in the strongest possible ways to prevent further atrocities. He added that Russia's delegation to the UN left "a trail of blood" whenever it entered the General Assembly hall.
The General Assembly is holding an emergency meeting following Russia's latest attacks. Although the session was convened because of the Kremlin's annexation of four partly-occupied Ukrainian regions following sham referendums, it has been overshadowed by this morning's attacks, BBC reported.
