Medvedev landed on Iturup, one of four islands in the chain that lies off Russia's far eastern coast and just north of Japan, Russian media reports said.
"Everything is perfectly modern here," Medvedev was quoted as saying on his arrival.
"This is the result of our development programme for the Kuril islands."
Hajime Hayashi, the head of the Japanese foreign ministry's European division, telephoned the Russian ambassador in Tokyo over the visit to the islands, which Japan calls the Northern Territories.
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Soviet troops seized the islands just after Japan surrendered in World War II.
The seven-decade-old dispute has hampered trade and prevented Moscow and Tokyo from signing a formal post-war peace treaty.
Both the Kremlin and Japanese Prime Minister Shinzo Abe had hoped to start mending relations in order to revive trade, with Japan seeking broader access to Russia's plentiful oil and natural gas supplies.
According to the Interfax news agency, Medvedev will visit a forum on the education of Russian youth and several economic projects on the archipelago, including Iturup Airport, which opened in September.
The cosmodrome is designed to ease Russia's dependence on space launches in Baikonur, in Kazakhstan.
Medvedev visited the islands in 2012, and Russia held military exercises there in 2014. Both incidents provoked protests from Tokyo.