Abe is hosting Putin in his ancestral city of Nagato in hopes of achieving a breakthrough over the territory off Japan's northern coast seized by Soviet troops in 1945.
The four islands are known as the Southern Kurils in Russia and the Northern Territories in Japan, and the dispute has been a thorn in relations for more than seven decades.
Abe would like to seal a deal as soon as possible because the islands' ageing Japanese former residents are dwindling in number.
"I want to go into this summit with determination to end the issue in my generation," Abe told former residents earlier this week, suggesting an agreement remains distant.
The two leaders shook hands before sitting down for their first meeting during the two days of talks, with Abe welcoming Putin to his hometown.
"I think the summit today and tomorrow will bring a big contribution to the development of ties," Putin said.
Putin, a judo fan who is making his first visit to Japan as president in 11 years, has said he wants to end the "anachronism" of the two countries not having a World War II peace treaty.
Underscoring the intense interest in the meeting in Japan, Putin's arrival at the airport in the city of Ube, about three hours later than originally anticipated, was shown live on television.
The summit is the latest attempt to draw a line under World War II since Japan and the Soviet Union began discussions in 1956.
Abe's late father Shintaro took the lead in negotiations with Moscow as a foreign minister but died in 1991 after pushing for talks while suffering from cancer.
In Nagato, Abe and Putin are expected to focus on territorial and peace treaty issues, a Japanese foreign ministry official said.
Abe has looked to eke out concessions by dangling the prospect of major Japanese investment in front of Moscow, which is mired in economic crisis.
But few believe Putin is likely to cave to Japanese demands to hand back at least some control over the islands, especially after Donald Trump's election as president of the United States last month.
The New York real-estate baron has vowed to improve ties with Russia, where the economy has reeled under US sanctions against Moscow over Ukraine and the impact of falling oil prices.
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