The Kremlin on Monday ruled out entering peace talks with Ukraine over Kyiv's surprise offensive into Russian territory, which Ukrainian President Volodymyr Zelensky said was meeting its goals.

Ukraine sent troops over the border on August 6 and has since held onto a part of the western Kursk region, in the biggest attack on Russian soil since Moscow attacked in February 2022.

The move has rattled Moscow and taken Ukraine's Western allies by surprise.

Kyiv has said the offensive is aimed at stretching Russian forces, creating a "buffer zone" and bringing the conflict "closer" to an end on "fair" terms.

Kremlin aide Yuri Ushakov said on Monday that it had pushed the prospect of peace talks further away.

"At the current stage, given this escapade, we will not talk."

He called entering a negotiating process "completely inappropriate" and said future talks "depend on the situation on the battlefield, including in the Kursk region."

Moscow, intent on not letting the offensive affect its own advance in eastern Ukraine, claimed another village in the war-battered Donetsk region on Monday.

Bracing for a further assault, Ukraine ordered the evacuation of families from the key city of Pokrovsk as Moscow's forces inched closer to the logistics hub.

Zelensky, meanwhile, said his troops in Kursk – who have set up administrative offices and published previously unthinkable footage of Ukrainian soldiers patrolling Russian streets – are meeting their targets.

"We are achieving our goals. This morning we have another replenishment of the (prisoner of war) exchange fund for our country," Zelensky said, referring to more Russian troops being taken prisoner.

On Sunday, Zelensky said the push into Russian territory was designed to create a "buffer zone."

The prospect of peace talks appeared distant even before Ukraine launched its incursion into Russia.

Russian President Vladimir Putin had demanded Ukraine cede swathes of territory if it wanted a ceasefire.

Zelensky, who has ruled out direct talks with the Kremlin, demands Russia's full withdrawal from Ukrainian territory, including Crimea, and reparations.

In recent days, Ukraine has destroyed two key bridges over the Seym river inside Russia, seeking to disrupt Moscow's supply routes to the combat zone.

A third bridge over the river was hit over the weekend, a Russian military investigator said in a video published by high-profile pro-Kremlin TV commentator Vladimir Solovyev.

The attacks on the bridges have left Russia with limited options, according to Russian military bloggers.

Moscow's defence ministry said on Monday Russia had thwarted Ukrainian attacks on three more villages in the Kursk region.

Russia has also been accused of sending inexperienced conscripts to protect the Kursk region, unwilling to redeploy experienced fighters from the frontlines in eastern Ukraine.

The incursion has visibly worried Russians, prompting some in Kyiv to hope that sentiment could turn the country against the Kremlin's more than two-year war.

"Accustomed to seeing the war as a television show, Russians are now seeing it up close and personal," Ukrainian presidential adviser Mykhailo Podolyak said on X.

"If you don't want to see the war, you have to end the war by forcing your 'leadership' to make peace on fair terms."

In eastern Ukraine's Donetsk region, Moscow said it captured the town of Artemovo, which is called Zalizne in Ukraine.

Zalizne had a population of around 5,000 at the start of 2022 – making it one of the largest places captured by Russian troops in recent weeks.

Ukraine also said Russian attacks killed four people in frontline towns on Monday, with a 71-year-old woman killed in her garden in Toretsk and three civilians in their 60s and 70s killed in the village of Zarichne.

As the front moved further west towards the city of Pokrovsk, Ukrainian officials announced the compulsory evacuation of families with children.

"We are starting the forced evacuation of families with children from the Pokrovsk community," Donetsk governor Vadym Filashkin said, ordering the "compulsory" evacuation of children and their parents from Pokrovsk and about a dozen surrounding villages.

He said more than 53,000 people live in the area, including almost 4,000 children.

Filashkin called the decision to evacuate "necessary and inevitable."

Russia has long tried to capture Pokrovsk, which lies on the intersection of a key road that supplies Ukrainian troops. (AFP)