In a TV address on Friday, Ukraine's interim President Alexander Turchynov said Moscow wanted the new government to react to provocations so it could annex Crimea, BBC reports.
He appealed to Russian President Vladimir Putin to "stop provocations and start negotiations".
He said Russia was behaving as it did before sending troops into Georgia in 2008 over the breakaway regions of Abkhazia and South Ossetia, which have large ethnic Russian populations.
"They are implementing the scenario like the one carried out in Abkhazia, when after provoking a conflict, they started an annexation of the territory," Mr Turchynov said.
However, Russia's ambassador to the UN, Vitaly Churkin, said that any Russian military movements in Crimea were within Moscow's long-standing arrangement with Ukraine on the deployment of military assets.
"We are acting within the framework of that agreement," he said, after a closed-door meeting of the UN Security Council.