Nearly five weeks into an invasion in which it has failed to capture any major cities, Russia said it would curtail operations near Kyiv and the northern city of Chernihiv "to increase mutual trust" for peace talks.

But Chernihiv's Mayor Vladyslav Astroshenko said on Wednesday Russian bombardment had only intensified over the past 24 hours, with more than 100,000 people trapped in the city with just enough food and medical supplies to last another week.

"This is yet another confirmation that Russia always lies," he told CNN in an interview.

"They actually have increased the intensity of strikes," with "a colossal mortar attack in the centre of Chernihiv" on Wednesday wounding 25 civilians.

In an overnight address, Ukraine's President Volodymyr Zelenskiy made clear he took nothing Moscow said at face value.

"Ukrainians are not naive people," he said. "Ukrainians have already learned during these 34 days of invasion, and over the past eight years of the war in Donbas, that the only thing they can trust is a concrete result."

The past week has seen Ukrainian forces make substantial gains, recapturing towns and villages on the outskirts of Kyiv, breaking the siege of the eastern city of Sumy and pushing back Russian forces in the southwest.

The Pentagon said Russia had started moving very small numbers of troops away from positions around Kyiv, describing the move as more of a repositioning than a withdrawal.

"We all should be prepared to watch for a major offensive against other areas of Ukraine," spokesman John Kirby told a news briefing. "It does not mean that the threat to Kyiv is over."

Britain's defence ministry said Moscow was being forced to pull troops from the vicinity of Kyiv to Russia and Belarus, to resupply and reorganise after taking heavy losses.

Moscow has said in recent days that its main focus is now on southeastern Ukraine, a region called the Donbas, where it is trying to capture more territory to turn over to separatists it has supported since 2014.

The area includes Mariupol, a port of 400,000 people which has been lain to waste after a month of Russian siege, and where the United Nations believes thousands of people may have died.

On Wednesday, Russian forces were shelling nearly all cities along the front line separating Ukrainian government-controlled territory from areas held by the separatists in the region, the Donetsk governor said, and heavy fighting was reported in Mariupol.

The United Nations said on Wednesday that the number who have fled Ukraine had risen above 4 million. More than half of those refugees are children and the rest mostly women.

Russia and Ukraine held their first face-to-face peace talks in nearly three weeks at a palace in Istanbul on Tuesday. Ukraine presented a peace proposal under which it would accept neutral status with international guarantees to protect it from future attack. The proposal called for a ceasefire, and would postpone discussion of Russia's territorial demands.

Kremlin spokesman Dmitry Peskov said on Wednesday it was good to have the Ukrainian proposal in writing but there was no indication yet of a breakthrough. Russia could not negotiate over Crimea, which it seized and annexed in 2014, he said.

Western sanctions have isolated Russia from world trade to a degree never before visited on such a large economy. But Russia is still a major supplier of oil and gas to Europe, and Moscow has been trying to press that leverage.

Last week Moscow told Western buyers of its gas that they would now have to pay with roubles, a demand rejected by the G7 group of industrialised democracies.

Australian Associated Press