Russia has been widely condemned after bombarding cities across Ukraine, including launching missile strikes on the centre of Kyiv for the first time by Paul Adams in Kyiv and Elsa Maishman and Oliver Slow in London.
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.
US President Joe Biden was one of many foreign leaders to speak with President Zelensky, and he "pledged to continue providing Ukraine with the support needed to defend itself, including advanced air defence systems", the White House said.
Mr Biden said the attacks demonstrated "the utter brutality" of Putin's "illegal war".
After the phone call, President Zelensky vowed to strengthen Ukraine's armed forces and "make the battlefield even more painful for the enemy".
China and India, which have not condemned the war, called for a de-escalation.
ON THE GROUND: Shock and horror as playgrounds and bridges hit
BACKGROUND: Who - or what - blew up the Crimean bridge?
IN RUSSIA: Russian hawks celebrate deadly response to setbacks
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.
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Image source, Getty Images.
Monday's strikes saw central Kyiv targeted for the first time