Kyiv, Ukraine - People have been killed and injured in a wave of Russian missile attacks on the capital Kyiv and other major Ukrainian cities, President Volodymyr Zelensky said, as officials called on citizens nationwide to seek shelter amid the ongoing bombardment.

The attacks are seen as the Kremlin's revenge for the weekend explosion that damaged the strategically important bridge connecting the annexed Crimean peninsula to mainland Russia.

"At this stage, the death of five and the injury of 12 Kyiv residents are confirmed," Interior Ministry adviser Anton Gerashchenko said on his Telegram channel.

A children's playground was among the Kyiv sites affected by the missile fire, Gerashchenko added. Emergency workers were tending to injured people and extinguishing burning cars, video showed.

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Zelensky said that Russia was trying to totally destroy Ukraine and that ordinary people on their way to work during the Monday morning rush had been killed.

Kyiv Mayor Vitali Klitschko urged residents to seek shelter amid the missile fire, which he said was likely to continue. He stressed that emergency responders remained on duty despite the danger.

"Take warm clothes, water, a supply of food and chargers for phones," he advised of those heading to emergency shelters, which in Kyiv often means underground metro stations.

Several explosions were heard in Kyiv on Monday morning, sending plumes of smoke over the city center. Witnesses said areas continued to be hit by explosions some two hours after the first was heard.

Ukraine's capital has been hit by Russian missiles several times since the beginning of the war on February 24. But Monday's was the worst incident of its kind and the first attack on the Kyiv in months.

Rocket attacks were also reported in other parts of Ukraine, from Lviv in the west to areas of the more hotly contested east. Air raid warnings sounded almost nationwide, urging Ukrainians to seek shelter, and city mayors called on people to seek out bomb shelters.

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In the south-eastern Dnipropetrovsk region, governor Valentyn Reznichenko said there were a number of dead and injured following attacks around the industrial city of Dnipro.

Reznichenko called on residents of the area to get to bomb shelters. The Dnipropetrovsk town of Nikopol and Marhanets had also come under attack, he wrote on the Telegram messenger app.

Missile impacts were also reported by authorities in the western cities of Lviv and Khmelnytsky, and Zhytomyr in the north.

The south-eastern city of Zaporizhzhya, home to Europe's biggest nuclear plant, was also on alert after overnight rocket attacks.

Four deaths were reported by authorities as a result of a missile strike in the eastern Ukrainian city of Sloviansk in the Donetsk region. The impact occurred in the centre of the city, Mayor Vadim Lyakh said.

In Lviv, electricity has been knocked out in several areas, mayor Andriy Sadovyi said after several explosions were heard.

On Saturday, an explosion sparked a fire on the Kerch Bridge to Crimea, causing massive damage to the structure's train tracks and roadway.

The bridge is a key supply route for the Kremlin's faltering war, linking Russia to the Crimean peninsula that was illegally annexed by Moscow several years ago.

The blast prompted a shake-up of security by Russia and celebrations among Ukrainian officials, although Kyiv has not officially admitted involvement in the attack.

While Moscow said on Sunday that rail traffic was up and running again, Western experts say the bridge's reduced capacity will impact Russia's war efforts.

Putin has called the bridge explosion "an act of terrorism" and blamed Ukraine's SBU security service.

Late Sunday, former Russian president and prime minister Dmitry Medvedev called for the "annihilation of the terrorists" behind the attack.

Russia's Security Council, which Medvedev serves as the deputy head of, was due to meet on Monday.

Later on Monday, the UN General Assembly will deliberate on Russia's recent annexations of parts of Ukraine in defiance of international law.

At the end of the session in New York, which could drag on through Wednesday due to a large number of speakers, the body is expected to vote on a resolution condemning Moscow.