Russian forces are being pushed back around Kyiv but fighting is still fierce in some areas near Ukraine's capital, Ukrainian officials said today.
Russia said during negotiations last Tuesday that it would scale down operations in the Kyiv and Chernihiv regions, both of which are in northern Ukraine.
But officials in both regions say fighting has continued in some areas.
Reuters was unable to verify the information about military movements or fighting in Ukraine.
NATO Secretary-General Jens Stoltenberg has said Russian forces are not withdrawing but regrouping, and Ukrainian officials say Russian troops are losing ground rather than retreating of their own accord.
"Our troops are chasing them both to the northwest and northeast (of Kyiv), pushing the enemy away from Kyiv," said Oleksiy Arestovych, a political adviser to President Volodymyr Zelensky.
Mr Arestovych said Russia was carrying out a partial troop rotation and sending some of its forces to fight in eastern Ukraine.
The Kyiv region's governor, Oleksandr Pavlyuk, wrote on the Telegram messaging app earlier today that some Russian troops had moved back and were heading towards the border with Belarus, a Russian ally.
He said Russian forces had left the village of Hostomel, which is next to an important airport, but were digging in at the town of Bucha.
Mayor Vitaliy Klitschko later urged residents not to head back to Kyiv yet because "huge" battles were being fought to the north and east of the capital.
He did not indicate that these were new battles.
"The risk of dying is pretty high, and that's why my advice to anyone who wants to come back is: Please, take a little bit more time," he said.
Chernihiv Governor Viacheslav Chaus said some Russian troops had pulled back but some remained in his region.
"Air and missile strikes are (still) possible in the region, nobody is ruling this out," he said in a video address.
Ukrainian officials also said the besieged southern port city of Mariupol was still holding out after weeks of bombardment by Russian forces and that fighting continued in eastern Ukraine.
The Red Cross said the team it sent to facilitate the evacuation of thousands of civilians from Mariupol today had been forced to turn around after conditions made it "impossible to proceed".
"The ICRC team, which consists of three vehicles and nine personnel, did not reach Mariupol or facilitate the safe passage of civilians today," the International Committee of the Red Cross said in a statement, adding: "They will try again on Saturday to facilitate the safe passage of civilians from Mariupol."
Mariupol has been encircled since the early days of the Russian invasion of Ukraine that began on 24 February. Previous efforts by aid agencies to secure access have failed.

The Mariupol mayor said this week that up to 170,000 residents were trapped there without power and dwindling supplies while the UN human rights team is probing reports of mass graves.
Ukraine and Russia have resumed peace talks in an online format, Ukraine's presidential office has said, citing Ukrainian negotiator Mykhailo Podolyak but without providing further details.
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Meanwhile, Russia has accused Ukraine of carrying out its first airstrike on Russian soil, further dashing hopes of any de-escalation in President Vladimir Putin's war against Ukraine.

Russia said Ukrainian helicopters had hit Rosneft's fuel storage facility in the western town of Belgorod, around 40km from the border with Ukraine.
"There was a fire at the petrol depot because of an air strike carried out by two Ukrainian army helicopters, which entered Russian territory at a low altitude," Belgorod region governor Vyacheslav Gladkov wrote on messaging app Telegram.
The consequence of the accusation was swiftly made clear by the Kremlin.
"Of course, this is not something that can be perceived as creating comfortable conditions for the continuation of negotiations," Kremlin spokesman Dmitry Peskov told reporters, referring to ongoing peace talks.

Russia launched its offensive on 24 February on its neighbour, expecting to quickly take Kyiv and topple Mr Zelensky's government.
But a ferocious Ukrainian fightback and logistics and tactical problems scuppered such plans. Meanwhile Russia has faced unprecedented Western sanctions that have led multinationals to quit the country en masse.
With his economy crippled by unprecedented international sanctions, Mr Putin has sought to leverage Russia's status as an energy power, and warned that EU members will need to set up rouble accounts from today to pay for his country's gas.
"If such payments are not made, we will consider this a breach of obligations on the part of our buyers" and existing contracts would be stopped, Mr Putin said.
The EU has joined the United States in imposing sanctions, and European Parliament President Roberta Metsola is expected in Kyiv today in a show of support.
But the bloc has not imposed an energy embargo, and Germany, which imported 55% of its gas supplies from Russia before the war, insisted it will pay in euros or dollars as stipulated in contracts.