Relations between Moscow and Tokyo have been strained for decades over of the status of four Pacific islands near Japan's north coast, known as the Southern Kurils in Russia and the Northern Territories in Japan.
"The main area where our positions concur is the clear-cut political striving of our leaders for a mutually acceptable resolution," Lavrov said after talks with his Japanese counterpart Fumio Kishida in Moscow.
"We have an interest in resolving this protracted problem," Lavrov said, while admitting: "it's clear that it's not simple to bring the two sides' positions closer."
Kishida said the talks were "meaningful, important and useful" ahead of a visit he called the most important event in the countries' relations this year.
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The row dates from the end of World War II when Soviet troops seized the southernmost islands in an archipelago off the northeast coast of Hokkaido just after Japan surrendered.
Russia prompted protests from Japan last month by deploying coastal missile systems to boost its military presence on the islands.
"On the question of the peace treaty, we would like to reach a result that would be welcomed by the people both of Japan and Russia," Kishida said in comments translated into Russian.
He said he wanted "energetic talks" to "finally resolve the sovereignty of the four islands in a mutually acceptable form and conclude a peace treaty."
He said they agreed "to continue the line that our leaders agreed on the utmost all-round development of our relations in all spheres without exception.