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"Such moves go against our country's stance and is extremely regrettable," said Japan's chief Cabinet secretary Yoshihide Suga during a press conference Tuesday.
The 56-island Kuril chain has been a sore spot in Japan-Russia relations for the past 72 years.
The chain became part of Russia with the dissolution of the Soviet Union in 1991 but Japan claims four islands it refers to as the "Northern Territories."
The long-standing territorial dispute has prevented both countries from signing a peace treaty to end World War II.
The two leaders also discussed the possibility of joint economic activities on the islands.
Tokyo's response
Some analysts say Abe's administration is obliged to issue a response to the namings to assuage the right-wing nationalists that prop up the government, however Tokyo is unlikely to want to jeopardize diplomatic relations with Moscow.
"Abe is supported by right-wing nationalists. That means that he can't be weak on this," Atsushi Tago, a professor of international relations at Kobe University, told CNN.
"I think Abe likes to maintain the current agreement over joint Russian-Japanese economic activities, so he does not want to over-politicize this type of issue," added Tago.
Controversial names
The Russians have named the five islands after Andrei Gromyko, a Soviet diplomat, Igor Farkhutdinov, a former governor of the Sakhalin region, Anna Shchetinina, a female captain of a merchant ship, Gen. Kuzma Derevyanko, who signed the Japanese Instrument of Surrender with the Allies in 1945 and Gen. Alexei Gnechko, who led the occupation of the Kuril Islands in the same year, according to TASS, a Russian news agency.
The last two, according to James D Brown, an associate professor at Temple University in Japan, are a particular blow to the Japanese government.
"They're designed to make a political point," said Brown.
Disappointing for Tokyo
Tokyo has been trying to improve Japan-Russia relations and foster great economic relations since May 2016 when Abe visited Putin in Sochi, Russia.
In recent years, Putin has also been looking to shore up ties in Asia as part of what analysts have called Russia's "turn to the east" as US and European sanctions following Russia's annexation of Crimea took a toll.
"The momentum was building," said Brown, citing Putin's visit to Japan in December 2016. "But now Japan feels like their diplomatic efforts have been undermined."