The separatists’ appeal to Moscow was in a May 12 statement read out at a news conference by Denis Pushilin, a separatist leader in the self-declared "Donetsk People's Republic."
The move came a day after the Donetsk and Luhansk regions held so-called self-rule referendums.
The self-styled separatist officials – some of whom are now being targeted by EU sanctions -- claimed a high voter turnout and an overwhelming support for independence in the May 11 votes.
They also said there will be no voting in Ukraine's May 25 presidential election in the regions.
EU foreign policy chief Catherine Ashton has suggested that any disruption of the May 25 election could trigger further sanctions.
There were no official international election monitors to observe the May 11 votes.
Ukraine's government and Western nations have rejected the referendums.
The White House said the referendums are illegal.
U.S. State Department spokeswoman Jen Psaki said the voting "was an attempt to create further division and disorder” in Ukraine.
EU President Herman Van Rompuy, on a visit to Kyiv on May 12, said the European Union also does not recognize the “so-called referendums” which he called "illegal, illegitimate, and not credible."
He also said the EU was prepared to take "additional, far-reaching steps" if Russia failed to take steps that help resolve the conflict.
The EU’s expanded sanctions target 13 more individuals as well as two Crimea-based companies.
That brings to 61 the number of individuals from Russia, eastern Ukraine, and Crimea who face EU travel bans and asset freezes.
The expanded EU list includes officials involved in Russia’s annexation of Crimea -- such as Vyacheslav Volodin, first deputy chief of staff of Russian President Vladimir Putin; Vladimir Shamanov, commander of the Russian Airborne Troops; Vladimir Pligin, head of the Duma Constitutional Law Committee; and Pyotr Jarosh, acting head of the Federal Migration Service office for Crimea.
It also includes pro-Russian separatist leaders in eastern Ukraine -- such as Viacheslav Ponomaryov, the self-declared mayor of Slovyansk; Igor Mykolaiovych Bezler, head of a separatist militia in Donetsk; and Roman Lyahin, the head of the self-proclaimed “Central Election Commission of the Donetsk People's Republic.”
The two Crimea-based firms added to the growing EU sanctions list are PJSC Chernomorneftgaz and Feodosia. Both Ukrainian state firms were effectively confiscated by Crimea’s new self-appointed "authorities" after the region's annexation by Russia.
The Russian government said the results of the May 11 referendums should be "implemented in a civilized manner" and urged Ukrainian officials in Kyiv to engage in talks with the separatists.
Ukraine's acting President Oleksandr Turchynov earlier on May 12 called the votes in Donetsk and Luhansk a "farce" without any legal basis.
The Russian president’s office said in a statement that "Moscow respects the expression of the people's will" in Donetsk and Luhansk.
Russian Foreign Minister Sergei Lavrov said there was no further point in talks to resolve the Ukraine crisis without the involvement of separatist leaders.