Sergei Lavrov told journalists: "Russia and Cyprus have a common vision of the situation surrounding Kosovo. Independence unilaterally proclaimed by the Serbian province has failed to improve stability in the region."
Lavrov said Russia and Cyprus believed Belgrade and Pristina should resume talks to find a solution to the territorial dispute in line with international law.
Markos Kyprianou said Cyprus would not recognize Kosovo, which declared independence in February and has been backed by the United States and the majority of European Union countries.
"Cyprus does not intend to recognize Kosovo as an independent state," Kyprianou said, adding that the decision on Kosovo "should be reached within the UN framework and with Serbia's direct participation."
Moscow has sided with Belgrade in refusing to recognize the Albanian-dominated region. China, India, Spain, Greece, Brazil and certain other states have also refused to recognize Kosovo's independence.
Lavrov said Russia would actively support interaction between the Greek and Turkish communities in Cyprus aimed at settling the Northern Cyprus problem.
Cyprus has been divided since 1974, with the internationally recognized Republic of Cyprus in the south and the unrecognized Turkish Republic of Northern Cyprus in the north.
The Cyprus resolution halted in 2004 when a peaceful settlement plan put forward by then UN secretary general Kofi Annan failed at a referendum. Cypriot Turks agreed to the plan while Cypriot Greeks rejected it.
"Russia welcomes the dialogue that has resumed between the sides and will actively support efforts aimed at its development and successful completion," the Russian minister said, adding that the central role in the Cyprus problem settlement should belong to the UN.
Lavrov also said the Cypriot president would visit Russia in the second half of the year.