The Kremlin voiced its hope in a statement that "the practical implementation of the referendums results will take place in a civilized way," without violence.
It added that the Organization for Security and Cooperation in Europe could help organize a dialogue between Ukraine's government and representatives of the east, where about 90 percent of votes backed sovereignty for their regions in Sunday's vote.
The statement signaled that Russia has no intention to annex the Donetsk and Luhansk provinces, like it annexed Crimea following a similar referendum in March.
It also noted the "high turnout" in the vote and condemned the use of force against civilians in the east.
According to early returns, 89 percent of those who cast ballots Sunday in the Donetsk region and about 96 percent of those who turned out in the neighboring Luhansk region voted for expanded sovereignty.
The pro-Russian insurgents who organized the vote said the ultimate status of the regions would be discussed later and could include the possibility of secession or annexation by Russia.
Sky News reported that organizers of the vote distributed three million ballot papers across the two regions.
Election organizers told the Associated Press that turnout topped 70 percent by late afternoon Sunday, but with no international election monitors in place, it was all but impossible to confirm such claims.
Ukraine's central government and the West have condemned the balloting as a sham and a violation of international law, and accused Moscow of fomenting the unrest in a possible attempt to grab more land weeks after the annexation of Crimea.
"The farce, which terrorists call the referendum, will have no legal consequences except the criminal responsibility for its organizers," Ukraine's acting President Oleksandr Turchynov said in a statement Monday.
Russian President Vladimir Putin had urged the organizers to postpone the vote in an apparent attempt to distance himself from the insurgents and keep his hands free for bargaining with the West on defusing the crisis.
His spokesman, Dmitry Peskov, was quoted by the Kommersant daily Monday as saying that it was difficult for people in the east to heed Putin's call because of fighting in the region.
Putin had not yet commented on the voting as of midday Monday.
The insurgents in the east have seized government buildings and clashed with government troops and police over the past month.
More than 30 people have been reported killed since Ukrainian forces began trying to retake some eastern cities from the insurgents.
Sunday's voting in the two regions with a combined population of 6.5 million appeared mostly peaceful, but armed men identified as members of the Ukrainian national guard opened fire on a crowd outside the town hall in Krasnoarmeisk, and an official with the region's insurgents said people were killed.
It was not clear how many.
The bloodshed took place hours after dozens of armed men shut down the voting in the town.
Witnesses to the shooting posted a number of videos on YouTube.
One of the videos shows several armed men holding AK-47s yelling to the crowd "go home, get out of here."
One then cocks his weapon, and seconds later a man from the crowd steps forward and approaches another gunman, also carrying an AK-47, to speak with him.
The gunman fires a warning shot over his head, but that doesn't deter the man.
He continues to approach as shots continue and the man is struck by a bullet, falls to the ground and can be seen bleeding from his leg.
The video, shot by someone at the scene of the confrontation, has been authenticated based on accounts by AP journalists at the site and was consistent with AP's own reporting on what happened.
The Ukrainian Defense Ministry said an army soldier was wounded in a mortar shelling near Slavyansk TV tower shortly before voting began Sunday.
The city's self-proclaimed mayor, Vyacheslav Ponomaryov told Sky News that turnout was 80% and the result "was not in doubt".
Asked if he knew what would follow, the former businessman said:
"Of course we know. Work starts on the establishment ... of the Donetsk People's Republic."
Western leaders have threatened more sanctions in the key areas of energy, financial services and engineering if Moscow continues what they regard as efforts to destabilize Ukraine.
The European Union may announce new measures endorsing a widening of the legal criteria for imposing sanctions on Russia as early as Monday, with the goal of making it easier to freeze the assets of companies involved in the Ukraine crisis.
Using the new expanded criteria, E.U. officials have prepared a list of 14 people and two Crimean companies active in the energy sector that ministers are likely to add to the E.U. sanctions list today, diplomats say.
The identities of the people and firms are being kept confidential for now.
The E.U. has previously imposed asset freezes and visa bans on 48 Russians and Ukrainians over Moscow's annexation of Crimea but it would be the first time the bloc has targeted companies.
Source: FOX News