Russia has called on Ukraine to halt its military offensive against pro-Moscow rebels in the east after giving its backing to contentious elections held in the separatist regions.

Grigory Karasin, Russia's deputy foreign minister, on Monday said the leaders elected on Sunday in polls not recognised by Kiev or the EU "have enough authority to establish broad sustainable dialogue with Kiev authorities," the Russian state news agency TASS reported.

"This work can bring results only on condition of equal dialogue based on mutual respect, with Kiev renouncing military operations and the notorious 'anti-terror operation'," Karasin was quoted as saying.

In the vote, residents in Donetsk and Luhansk were asked to choose legislators and executives.

Plans for the vote had been sharply criticised by the EU and the US, which said it violated Ukrainian law and undermined a two-month old ceasefire deal, which both sides have accused the other of breaking on multiple occasions.

Still reeling from Russia's annexation of its Crimean Peninsula in March, Ukraine accuses Moscow of undermining its sovereignty.

Russia appeared to hint in a 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 towards promoting sustained dialogue between central Ukrainian authorities and the representatives of the Donbass," the Russian statement said.

Results on 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.

Roman Lyagin, the head of the rebel election body in Donetsk, 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 recognise the result of our vote or not is Kiev's problem."

Votes 'not accepted'

Despite the ceasefire 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."

Source: Agencies