Japanese Prime Minister Shinzo Abe is in Russia for the two nations’ first top-level talks in a decade.
Discussions are set to focus on energy deals and a territorial row unresolved since the end of World War II.
Ahead of the visit, Mr Abe said he wanted to build “a trusted personal relationship” with President Vladimir Putin.
He also said he wanted to revive talks on a post-war peace deal – something so far prevented by the territorial row.
“I will work on boosting Japan-Russia relations so that this visit will mark a restart in stalled negotiations over a peace treaty,” Mr Abe said ahead of his flight to Moscow.
The dispute centres on four islands north of the Japanese island of Hokkaido, which Russia calls the Southern Kurils and Japan calls the Northern Territories.
Russia has controlled the islands since Soviet troops seized them from Japan at the end of World War II.
Prime Minister Dmitry Medvedev has visited the islands twice in recent years, causing anger in Japan.
In February, Japan scrambled fighters in response to what it said was an intrusion into its airspace by Russian fighters near the islands, as Mr Abe made a speech on the territorial row.
But energy is also set to be discussed, as Japan works to diversify its energy supply in the wake of the Fukushima nuclear disaster that has left almost all of its nuclear reactors suspended.
It is already a major importer of liquefied natural gas, including from the Russian Far East island of Sakhalin.
Possible Japanese investment in a liquefied natural gas hub in Vladivostok, connected by a pipeline to gas fields in East Siberia, could be discussed, reports say.
Prior to this visit Junichiro Koizumi was the last Japanese leader to visit Moscow, in 2003. After Russia, Mr Abe heads to Turkey and the Middle East.