US President Joe Biden has condemned the “utter brutality” of Vladimir Putin’s war as Russia unleashed a wave of missiles on major Ukrainian cities in deadly revenge for its humiliation.

A barrage of missiles rained down during rush hour in Ukraine, shattering the relative normality in cities like Kyiv in what was described as the widest bombardment since the war began.

Ukraine and Russia say the attacks were aimed at energy infrastructure, but the weapons also tore into busy intersections, parks and tourist sites in the capital Kyiv.

Explosions were reported in Lviv, Ternopil and Zhytomyr in Ukraine’s west, Dnipro and Kremenchuk in central Ukraine, Zaporizhzhia in the south and Kharkiv in the east.

In Kyiv, the body of a man in jeans lay in a street at a major intersection, surrounded by flaming cars.

In a park, a soldier cut through the clothes of a woman who lay in the grass to try to treat her wounds. Two other women were bleeding nearby.

A huge crater gaped next to a children’s playground in a central Kyiv park. The remains of an apparent missile were buried, smoking in the mud.

A gaping hole in a children’s park in Kyiv. Photo: Getty

Pedestrians huddled for shelter at the entrance of Metro stations and inside parking garages.

At the latest update on Tuesday morning (Australian time) 11 people had died and 89 were injured.

The attacks were furious retaliation for a blast on the Russian-built bridge to the annexed Crimea peninsula at the weekend which has been a major embarrassment to the Kremlin.

Ominous threat

In a foreboding signal that Russia’s revenge is not over, former president Dmitry Medvedev warned “there will be others” as long as Ukraine posed a “constant, direct and clear threat to Russia”.

“Therefore, in addition to protecting our people and protecting the country’s borders, the goal of our future actions, in my opinion, should be the complete dismantling of the political regime of Ukraine,” he posted on Telegram.

Mr Biden said the missile strikes “once again demonstrate the utter brutality of Mr Putin’s illegal war on the Ukrainian people”.

“These attacks only further reinforce our commitment to stand with the people of Ukraine for as long as it takes,” Mr Biden said in a statement.

“Alongside our allies and partners, we will continue to impose costs on Russia for its aggression, hold Putin and Russia accountable for its atrocities and war crimes, and provide the support necessary for Ukrainian forces to defend their country and their freedom.”

Ukraine’s emergency services said critical infrastructure was hit in 12 different regions and disrupted electricity in 15 regions, including Lviv, Kyiv and Zaporizhzhia.

Ukraine’s President Volodymyr Zelensky said the rush-hour attacks appeared to have been deliberately timed to kill people.

By mid-morning, Ukraine’s defence ministry said Russia had fired 75 cruise missiles, and Ukraine’s air defences had shot down 41 of them.

Security camera footage posted online showed a cloud of shrapnel and flame engulfing a glass-bottomed footbridge across parkland in the city centre, one of Kyiv’s most popular tourist sites.

The bridge appeared to have been empty at the time.

“They are trying to destroy us and wipe us off the face of the Earth,” Mr Zelensky said on the Telegram messaging app.

“The air raid sirens do not subside throughout Ukraine. There are missiles hitting. Unfortunately, there are dead and wounded.”

He later said the strikes had two main targets: Energy infrastructure, and people.

“Such a time and such targets were specially chosen to cause as much damage as possible.”

There was no immediate word from Moscow on what it was targeting.

Russia denies deliberately targeting civilians.

At one of Kyiv’s busiest road junctions, a massive crater had been blown in the intersection. Buildings were damaged and two cars and a van near the crater were completely wrecked, blacked and pitted from shrapnel.

Windows had been blown out of buildings at Kyiv’s main Taras Shevchenko University.

National Guard troops in full combat gear and carrying assault rifles were lined up outside an education union building.

The strikes came two days after an explosion damaged the only bridge over the Kerch Strait to the Crimea peninsula, which Mr Putin on Sunday called “an act of terrorism aimed at destroying critically important civilian infrastructure”.

“This was devised, carried out and ordered by the Ukrainian special services,” he said in a video on the Kremlin’s Telegram channel.

Ukraine has not claimed responsibility for the blast on the bridge but has celebrated it.

Senior Russian officials demanded a swift response from the Kremlin ahead of a meeting of Mr Putin’s security council on Monday.

The bridge, which Mr Putin personally opened, is a major supply route for Russian forces in southern Ukraine and a symbol of Russia’s control of Crimea, the peninsula it proclaimed annexed after its troops seized it in 2014.

Russia has faced major setbacks on the battlefield since the start of September, with Ukrainian forces bursting through the front lines and recapturing territory in the northeast and the south.

Mr Putin responded to the losses by ordering a mobilisation of hundreds of thousands of reservists, proclaiming the annexation of occupied territory and threatening repeatedly to use nuclear weapons.

-with AAP