Russia is in contact with the United States about a new round of talks on a Ukraine peace settlement as soon as conditions allow, the Kremlin said on Thursday.

"We remain open, we are in contact with the Americans, and we are counting on holding the next round of talks as soon as circumstances permit," Kremlin spokesman Dmitry Peskov said.

Peskov rejected the thesis of a New York Times opinion piece that said the Iran war had caused President Vladimir Putin to lose interest in negotiating an end to the Ukraine conflict.

"This is an absolutely false invention that does not correspond to reality. During the rounds of trilateral talks that have taken place, some progress was made toward a settlement," Peskov told reporters.

Peskov said Russia had not lost interest in peace talks but added that key issues - including territory - had yet to be settled.

The New York Times opinion piece, by Russian journalist Mikhail Zygar, said Russia's economy had been faltering earlier this year, prompting Putin at that point to take negotiations on a Ukraine settlement more seriously.

However, Zygar said the Iran war had reversed those dynamics by boosting oil prices, easing the economic pressure on Moscow and reducing the U.S. focus on Ukraine, weakening any incentive for the Kremlin to seek a settlement.

Earlier this week, Kremlin aide Yuri Ushakov said the U.S. had briefed Russia about Washington's latest round of talks with a Ukrainian delegation in Florida, which took place last Saturday.

The last three-way peace talks between Russia, Ukraine and the U.S. took place last month, before the Trump administration and Israel began airstrikes against Iran on Feb. 28.