Talks between the United States and Russia in Geneva were a "positive" start to continued dialogue amid tensions over Ukraine, the Kremlin said on Tuesday.

"This deserves a positive assessment," Kremlin spokesman Dmitry Peskov told reporters. 

"But this is not a process for the sake of process... what's important here is the result. There is nothing to say yet about the result."

Top US and Russian officials met in the Swiss city on Monday for the first meeting in a week of diplomatic activity between Russia and the West.

The high-stakes talks come amid fears of a Russian invasion of its pro-Western neighbour Ukraine. Moscow has demanded wide-ranging concessions from Washington and its NATO allies, which in turn have threatened severe sanctions for any attack.

Moscow denied at the talks that any attack was planned, despite massing tens of thousands of troops on Ukraine's border.

Both sides said there was no breakthrough at Monday's talks but they agreed to further dialogue.

"There are a few more rounds ahead to create a clear picture of where we are," Peskov said.

"There are not many reasons for optimism yet. It would be naive to believe that one round will give an exhaustive result," he said.

Monday's talks in Geneva launched days of intensive diplomacy between Russia and the West after the Russian troop movements on the border with Ukraine triggered a Cold War-style standoff.

A meeting of the NATO-Russia Council will take place in Brussels on Wednesday, then the permanent council of the Organisation for Security and Cooperation in Europe (OSCE) will meet in Vienna on Thursday with the issue of Ukraine expected to dominate.