President Vladimir Putin has yet to comment on the result of the referendum, but his spokesman Dmitry Peskov said he hoped the decision to leave the EU would not hurt Britain's bilateral ties with Russia.
"We have a very complicated history... In bilateral relations, we can't always say that our British partners are ready to communicate and cooperate," Peskov told journalists.
"We hope that in the new reality, the understanding of a necessity to build good relations with our country will prevail."
Many observers have said that Brexit would play into the hands of Putin who has been accused of driving a wedge between EU members.
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Moscow mayor Sergei Sobyanin said that a European Union without Britain would be less likely to maintain economic sanctions against Russia.
"Without Britain, nobody will keep fighting so hard for EU sanctions against us," he wrote on Twitter.
Peskov however made no indication that Moscow is pleased with the result of the vote.
"The EU is a very important trade, economic and investment partner of Russia, and Moscow is of course interested in the EU staying a big economic power, one that is flourishing, stable and predictable.