Ukraine has declared an air raid alert over the whole country and senior officials say air defences units are shooting down incoming Russian missiles, while fighting also intensified in Bakhmut in the east.
The attacks on Thursday come after the United States and Germany announced plans to arm Ukraine with dozens of modern battle tanks in its fight against Russia, which denounced the decisions as an "extremely dangerous" step.
"The first Russian missiles have been shot down," Andriy Yermak, head of President Volodymyr Zelenskiy's office said.
Overnight, the military said its anti-aircraft defences had shot down all 24 drones sent by Russia, 15 around the capital, Kyiv. There were no reports of damage.
Officials told the public to take shelter.
Russia has targeted critical infrastructure with missile and drone strikes since October, causing sweeping blackouts and other outages during the bitter winter.
Earlier, Zelenskiy praised the US and German commitments to send tanks and urged allies to provide large quantities of tanks quickly.
"The key now is speed and volumes. Speed in training our forces, speed in supplying tanks to Ukraine. The numbers in tank support," he said in a nightly video address on Wednesday.
"We have to form such a 'tank fist', such a 'fist of freedom'."
Ukraine has been seeking hundreds of modern tanks to give its troops the firepower to break Russian defensive lines and reclaim occupied territory in the south and east. Ukraine and Russia have been relying primarily on Soviet-era T-72 tanks.
The promise of tanks comes as both Ukraine and Russia are expected to launch new offensives in the war.
US President Joe Biden announced his decision to supply 31 M1 Abrams tanks hours after Berlin said it would provide Leopard 2 tanks - the workhorse of NATO armies across Europe.
Maintaining Kyiv's drumbeat of requests for more aid, Zelenskiy said he spoke to NATO Secretary General Jens Stoltenberg and called for long-range missiles and aircraft.
Ukraine's allies have already provided billions in military support including sophisticated US missile systems.
The US has been wary of deploying the difficult-to-maintain Abrams but had to change tack to persuade Germany to send to Ukraine its more easily operated Leopards.
Biden said the tanks pose "no offensive threat" to Russia and that they were needed to help the Ukrainians "improve their ability to manoeuvre in open terrain".
Germany will send an initial company of 14 tanks from its stocks and approve shipments by allied European states.
Russia reacted with fury to Germany's decision to approve the delivery of the Leopards.
"This extremely dangerous decision takes the conflict to a new level of confrontation," said Sergei Nechayev, Russia's ambassador to Germany.
Since invading Ukraine on February 24 last year, Russia has shifted its rhetoric on the war from an operation to "denazify" and "demilitarise" its neighbour to casting it as a face-off between it and the US-led NATO alliance.
Senior US officials said it would take months for the Abrams to be delivered and described the decision to supply them as providing for Ukraine's long-term defence.
Germany's tanks would probably be ready in three or four months, Defence Minister Boris Pistorius said.
Pledges to Ukraine from other countries that field Leopards have multiplied with announcements from Poland, Finland and Norway. Spain and the Netherlands said they were considering it.
Britain has offered 14 of its comparable Challenger tanks and France is considering sending its Leclercs.