Russia gave its backing Monday to a contentious election held by separatists in eastern Ukraine, setting the stage for renewed diplomatic tensions with the West.

The Foreign Ministry in Moscow said Sunday's vote in Donetsk and Luhansk gave elected representatives the authority to restore stability in regions unsettled by an armed separatist insurgency.

Plans for the vote had been sharply criticized by the EU and the U.S., which said it violated Ukrainian law and undermined a two-month old cease-fire deal. In the vote, residents in Donetsk and Luhansk were choosing legislators and executives.

Still reeling from Russia's annexation of its Crimean Peninsula in March, Ukraine accuses Moscow of undermining its sovereignty. Russia appeared to hint in its statement, however, that it would stop short of supporting outright independence for the Donbass, as Ukraine's heavily industrial eastern regions are known collectively.

"In view of the elections, it is extremely important to take active steps toward promoting sustained dialogue between central Ukrainian authorities and the representatives of the Donbass," the Russian statement said.

Vote results unveiled Monday showed Alexander Zakharchenko, the rebel leader in Donetsk, claiming an easy victory. The head of the separatists in Luhansk region, Igor Plotnitsky, won by a similarly large margin.

The head of the rebel election body in Donetsk, Roman Lyagin, said inescapable conclusions needed to be drawn from Sunday's polls.

"Kiev has to come to terms with the idea that Donbass is not part of Ukraine," he said. "Whether they will recognize the result of our vote or not is Kiev's problem."

Despite the cease-fire deal reached September in the Belarusian capital, Minsk, fighting rages daily between government troops and rebel forces in the Donetsk and Luhansk regions.

That agreement, which was signed by rebel leaders, and Ukrainian and Russian officials, envisioned local elections being held across the whole of the east, but under Ukrainian law.

On Monday, Germany's foreign minister reiterated that the EU would "accept neither the votes nor their results."

"It is clear that the Minsk agreement must be the standard for all efforts to deescalate the conflict," Frank-Walter Steinmeier said during a visit to Indonesia. "It is also clear that yesterday's so-called elections violate the letter and the spirit of the Minsk agreement."