"One of the aims of the visit is to prepare for Russian-Japanese contacts at the top level," Russian foreign ministry spokeswoman Maria Zakharova said.
Kremlin spokesman Dmitry Peskov told journalists it was "possible" Prime Minister Abe could visit Moscow in May.
Japanese-Russian have been hampered by a festering territorial dispute over four islands claimed by both countries.
Known as the Kuril Islands by Russia and the Northern Territories by Japan, the archipelago was seized by Soviet troops at the end of World War II just after Japan surrendered.
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Lavrov said in January that Putin and Abe had agreed that the question of a peace treaty between their two countries was on a list of issues "to be decided."
Japanese Foreign Minister Fumio Kishida visited Russia in September last year to discuss the islands, when he said the countries should "create a mutually acceptable solution to the territorial issue."
Russia said in December that it was building new modern compounds for its troops on two of the islands.
Russian Prime Minister Dmitry Medvedev visited one of the disputed islands, which are home to some 19,000 Russians, in November last year, infuriating Tokyo.