Mr Turchinov said the Kremlin was trying to disrupt a presidential election this month which is taking centre-stage in a confrontation pitting Moscow and the separatists against the government in Kiev and its Western backers.
A rebel leader in the eastern Luhansk region said it would boycott the May 25 election.
What he called the "Republic of Luhansk" may hold a further referendum on union with Russia, as Ukraine's Crimea region did under Russian military occupation before its annexation by Moscow in March.
Ukraine's election is intended to secure democratic continuity and legitimacy after pro-Moscow president Viktor Yanukovich fled the country in February.
Western governments have threatened more sanctions in the vital areas of energy, financial services and engineering if Moscow disrupts the vote.
Moscow said it respected the outcome of Sunday's referendums in which separatists claimed 90% support in the industrial Donetsk region and 96.2% backing in Luhansk region.
The results should be implemented peacefully, Russia said, without saying what further action it might take.
Eastern Ukraine has been plagued by turmoil as Kiev has tried to regain control of the largely Russian-speaking areas, and health authorities said 49 people have been killed in violence in the region of Donetsk since March 13. The EU declared the referendums illegal and increased pressure on Russia by taking a first step towards extending sanctions to companies, as well as people, linked to Crimea's annexation.
However cracks are appearing in the West's united front. Diplomatic sources said France will press ahead with a £1 billion contract to sell helicopter carrier ships to Russia.