The Kremlin said in a statement Monday, "Moscow respects the expression of the people's will in Donetsk and Luhansk."
Russian Foreign Minister Sergei Lavrov said de-escalating the crisis in Ukraine is only possible if Kiev and the separatists hold talks, rejecting the need for an international meeting.
Ukraine's interim president Oleksandr Turchynov has slammed the rebel-held referendums as a "propaganda farce without any legal basis."
Turchynov told Ukraine's parliament Monday the referendums were "nothing more than propaganda to cover up murders, kidnappings, violence and other serious crimes."
However, the president said he wanted to "continue dialogue with those in the east of Ukraine who have no blood on their hands and who are ready to defend their goals in a legitimate way."
European Union foreign ministers are meeting Monday to determine what additional sanctions to impose on Russia for its annexation of Crimea, Ukraine's province on the Black Sea and its perceived role in the unrest roiling Ukraine's east.
Organizers of the controversial independence referendums in the Donetsk and Luhansk regions said Monday about 90 percent of those voting have backed their call for sovereignty.
The results from Sunday's vote are impossible to verify.
It is still unclear whether so-called independence would mean more autonomy within Ukraine, an attempt to create an independent state, or a move to join Russia.
A VOA reporter in Donetsk described the election as a "shambles," with no clear procedures on tallying the ballots, reports of multiple voting, and makeshift ballot boxes.
Some who voted for independence say they mistrust the central Ukrainian government and believe a unified Ukraine is impossible.
Those who oppose secession say the whole election is illegal; most did not bother to cast a ballot.
A similar referendum in Ukraine's Crimean peninsula in March led to Russian annexation and the current crisis throughout eastern Ukraine, where pro-Russian separatists are in control of a number of towns and cities.
Meanwhile, Russian troops are massed at Ukraine's borders.
The German newspaper Bild am Sonntag reported Sunday that about 400 mercenaries hired by the U.S. security firm Academi are working for the fledgling Kiev government in its eastern Ukraine operations against the pro-Russian rebels.
The company, however, told VOA's Ukrainian service the report was "absolutely false."
Source: Voice of America