US President Joe Biden says civilian deaths caused by missile attacks across Ukraine illustrate the "utter brutality" of the war led by Russian President Vladimir Putin.

"The United States strongly condemns Russia's missile strikes today across Ukraine, including in Kyiv," a White House statement said.

"These attacks killed and injured civilians and destroyed targets with no military purpose. They once again demonstrate the utter brutality of Mr Putin's illegal war on the Ukrainian people."

Biden renewed a call on Russia to withdraw all of its forces from Ukraine.

Police block the scene of Russian shelling in Kyiv after two explosions following months of relative calm in the Ukrainian capital. Photo / Efrem Lukatsky, AP

"These attacks only further reinforce our commitment to stand with the people of Ukraine for as long as it takes," he said. "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."

Russia retaliated for what it claimed was a Ukrainian terrorist attack on a critical bridge by unleashing its biggest and most widespread attacks against Ukraine in months.

The lethal barrage against multiple cities smashed civilian targets, knocking out power and water, shattering buildings and killing at least 11 people.

Ukraine's Emergency Service said 64 people were wounded in the morning rush-hour attacks that Russia launched from the air, sea and land against at least 14 regions, spanning from Lviv in the west to Kharkiv in the east. Many of the attacks occurred far from the war's front lines.

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An injured woman leans against a wall for support after Russian shelling in Kyiv, Ukraine. Photo / Efrem Lukatsky, AP

Though Russia said missiles targeted military and energy facilities, some struck civilian areas while people were heading to work and school. One hit a playground in downtown Kyiv and another struck a university.

Andriy Yermak, a senior adviser to President Volodymyr Zelenskyy, said the strikes had no "practical military sense" and that Russia's goal was to cause a "humanitarian catastrophe".

Putin said his forces used "precision weapons" to target key energy infrastructure and military command facilities in retaliation for Kyiv's "terrorist" actions - a reference to Ukraine's attempts to repel Moscow's invasion forces, including an attack Saturday on a key bridge between Russia and the annexed Crimean Peninsula that Putin called a "terrorist act" masterminded by Ukrainian special services.

Police inspect the scene of Russian shelling in Kyiv. Photo / Efrem Lukatsky, AP

Putin vowed a "tough" and "proportionate" response should Ukraine carry out further attacks that threaten Russia's security. "No one should have any doubts about it," he told Russia's Security Council by video.

The Russian president has been under intense domestic pressure to take more aggressive action to stop a largely successful Ukrainian counter-offensive and to react forcefully to Saturday's attack on the Kerch bridge, whose construction he used to cement his 2014 annexation of Crimea.

Putin's increasingly frequent descriptions of Ukraine's actions as terrorist could set the stage for even more bold and draconian actions. But in his speech, Putin - whose partial troop mobilisation order last month triggered an exodus of hundreds of thousands of men of fighting age from Russia - stopped short of an expected escalation from what he calls a "special military operation" to a counterterrorism campaign or martial law.

Moscow's war in Ukraine is approaching its eight-month milestone, and the Kremlin has been reeling from humiliating battlefield setbacks in areas of eastern Ukraine it is trying to annex.

Bombed out vehicles in Kyiv after Russian missiles strike the Ukraine capital. Photo / Efrem Lukatsky, AP

The head of Ukraine's law enforcement said the latest attacks damaged 70 infrastructure sites, of which 29 are critical. The Ukrainian General Staff said 84 cruise missiles and 24 drones were used. Ukrainian forces shot down 56 aerial targets, it said.

Blasts struck in the capital's Shevchenko district, a large area in the centre that includes the historic old town and government offices, Mayor Vitali Klitschko said.

Some of the strikes hit near the government quarter in the capital's symbolic heart, where parliament and other major landmarks are located. A glass-covered office tower was significantly damaged, with most of its blue-tinted windows blown out.

Zelenskyy, in a video address, referred to the rush-hour timing of Monday's attacks, saying Russia "chose such a time and such targets on purpose to inflict the most damage".

The strikes sent residents of Ukraine's two largest cities - Kyiv and Kharkiv - into bomb shelters, including subway stations.

While air-raid sirens have continued throughout the war in cities across the country, in Kyiv and elsewhere, many Ukrainians had begun to ignore their warnings after months of calm.

Just as traffic was beginning to pick up Monday morning, a commuter minibus, known as a "marshrutka" - a popular alternative to the city's buses and subways - was struck near Kyiv National University. Nearby, at least one strike landed in Shevchenko Park, leaving a large hole near a children's playground.

A crater created by an explosion after a Russian attack in Kyiv. Photo / Efrem Lukatsky, AP

Another target was the Klitschko pedestrian bridge - a landmark in central Kyiv with its glass panels. Closed-circuit television footage showed a huge explosion under the bridge, with smoke rising, and a man running away after the blast, apparently unhurt. No significant damage to the bridge was immediately apparent.

Air raid sirens sounded in every region of Ukraine except Russia-annexed Crimea, for four straight hours.

Associated Press journalists saw multiple bodies at an industrial site on the outskirts of Dnipro city. Four people were killed and 19 injured in the city, officials said.

Witnesses said one missile landed in front of a bus during the morning rush hour, damaging the vehicle but not killing any passengers.

Natalia Nesterenko, a mathematician, saw one missile fly by her Dnipro apartment balcony as she was working in her kitchen, then she heard two explosions.

"It's very dangerous. I immediately called my kids to see how they are because anyone can be hit - women, children," she said.

Kharkiv was hit three times, Mayor Ihor Terekhov said. The strikes knocked out the electricity and water supply. Energy infrastructure was also hit in Lviv, regional Governor Maksym Kozytskyi said.

Three cruise missiles launched against Ukraine from Russian ships in the Black Sea crossed Moldova's airspace, said the country's foreign affairs minister, Nicu Popescu.

The attacks brought out a fresh bout of international condemnation of Russia.

The Group of Seven industrial powers scheduled a videoconference on the situation, which Zelenskyy will address.

French President Emanuel Macron expressed "extreme concern". British Foreign Secretary James Cleverly tweeted: "Russia's firing of missiles into civilian areas of Ukraine is unacceptable."

"Russia once again has shown to the world what it stands for. It is terror and brutality," said European Commission President Ursula von der Leyen.

Some feared the attacks may just be the first salvo in a renewed Russian offensive. As a precautionary measure, Ukraine switched all schools to online learning until at least the end of this week. Ukrainian Foreign Minister Dmytro Kuleba broke off an Africa tour and headed back to Ukraine.

In an ominous move, Belarusian President Alexander Lukashenko announced that he and Putin have agreed to create a joint "regional grouping of troops". He offered no details. His defence minister, Viktor Khrenin, later issued a video warning Ukraine not to provoke Belarus, but added: "We don't want to fight."

Lukashenko repeated his claims that Ukraine is plotting an attack on Belarus, sparking fears the stage is being set for pre-emptive action by Minsk.

- Adam Schreck & Hanna Arhirova, AP