Russia said Sunday that negotiators were making headway at talks to resolve fighting in Ukraine, more than two weeks after President Vladimir Putin ordered his army over the borders of its pro-Western neighbour.

Leonid Slutsky, a senior member of Russia's negotiating team, told the state-run television network RT that "significant progress" was made following several rounds of talks hosted on the border of neighbouring Belarus. 

"If we compare the positions of both delegations at the start of the talks and now, we see significant progress," he told the network according to Russian news agencies.

"My own expectations are that this progress could develop over the next few days into a unified position held by both delegations in documents to be signed," agencies cited him as saying.

Negotiators from Moscow and Kyiv have held several rounds of talks since Putin sent in troops to the country. Turkey this week hosted a first meeting between the Russian and Ukrainian foreign ministers.

Kremlin spokesman Dmitry Peskov said in comments carried by Russian news agencies that negotiations were scheduled to continue Monday.

Earlier Sunday, a senior Ukraine advisor and presidential aide, Mikhailo Podolyak, wrote on Twitter that Russia had stopped issuing "ultimatums" and instead "carefully listens to our positions".

Ukrainian President Volodymyr Zelensky said Saturday that Russia had adopted a "fundamentally different approach" in the talks.

Meanwhile Russian President Vladimir Putin this week said there had been "some positive shifts" in the dialogue and that negotiations were being held almost daily.

On Sunday President Zelensky walked to a Kyiv hospital to meet injured soldiers, handing out medals.