By Fredrik Dahl

VIENNA (Reuters) - Russia has for the first time backed the idea of deploying an OSCE monitoring mission in Ukraine, including Crimea, the chairman of the European rights and security watchdog said on Thursday, calling it a possible "big step forward".

The development was announced a day after Russian President Vladimir Putin discussed the crisis in Ukraine with Swiss Foreign Minister Didier Burkhalter, whose country chairs the Organisation for Security and Cooperation in Europe (OSCE).

Russia launched new military exercises near its border with Ukraine on Thursday, showing no sign of backing down in its plans to annex its neighbour's Crimea region despite a stronger than expected drive for sanctions from the European Union and United States.

At the OSCE's Vienna headquarters, however, Switzerland's envoy to the body that seeks to prevent conflicts on the continent said Russia supports "the idea of a rapid approval and rapid deployment of a special monitoring mission for Ukraine".

"This is clearly a positive development, absolutely," Ambassador Thomas Greminger told reporters after a meeting of OSCE envoys. But a number of issues remained to be clarified in negotiations between the OSCE's 57 member states, he said.

Switzerland has proposed sending about 100 monitors to Ukraine to look into human rights, ethnic issues, security and other factors to ease tensions after pro-Russian forces took control of Crimea.

Such a mission would require consensus among all members, giving Moscow veto power. Russian diplomats attending OSCE meetings over the last two weeks had said they had no instructions on the issue from their government, according to diplomats from other countries. That effectively blocked the plan.

But at Thursday's meeting, "all delegations without exception" expressed backing for the plan, Greminger said.

STILL DIFFERENCES OVER MANDATE

Greminger said he would try to "take advantage of this opportunity" and press ahead with negotiations aimed at having the monitors on the ground "as rapidly as possible".

Other diplomats cautioned that it was still too early to say whether there would be a unanimous decision to send a monitoring team to assess the situation on the ground.

"There are different views on what the mandate should look at," one European envoy said. "The (Swiss) draft mandate puts a lot of focus on Crimea and the Russians want that removed."

Greminger said one sticking point was how to define the "geographic scope" of the monitors' activities. Although Russia approved of a country-wide operation, it was still a matter of how to phrase that in any decision, he said.

There was no immediate comment from Russia. Moscow, which denies its troops have a role in the takeover of Crimea, says people there - a small majority of whom are ethnic Russians - should have the right to secede. Western states say a referendum in Crimea on joining Russia planned for Sunday is illegal.

The U.S. Ambassador to the OSCE, Daniel Baer, said an OSCE mission could look at some of the concerns that Russia has raised on Crimea but also include other parts of Ukraine.

"I think we are moving toward a consensus decision that would have a monitoring mission with a mandate to cover all of Ukraine, including the Crimean peninsula," he told reporters.

Moscow's ambassador "just now said that the Russian Federation is prepared to work toward a monitoring mission that can be deployed to Ukraine," Baer said. "I'm hopeful that they will indeed take this step and walk through that open door."

(editing by David Stamp)