The two countries have never officially struck a peace accord more than after 70 years after the end of the conflict amid a territorial dispute over four Japanese islands seized by Soviet troops at the war's conclusion.
"President Putin and I share the view that it is abnormal for our nations not to have a peace treaty 70 years since" the war, Abe said at his first press conference of the year.
"I will continue my dialogue with President Putin when opportunities arise," he added. "We will explore the most appropriate timing for his visit to Japan."
Putin has come under intense criticism from the United States and other democracies over Russia's annexation of Crimea and the conflict in eastern Ukraine, with the country's participation in the Group of Eight summits under suspension.
Abe is hosting a meeting of Group of Seven leaders in May. Putin is not expected to attend and Abe did not suggest otherwise.
"It is also important that we gain Russia's constructive engagement to deal with issues of terrorism, Syria and Iran," Abe said.
Russia has been waging air strikes in Syria since the end of September as it seeks to bolster the regime of Syrian President Bashar al-Assad and prevent Islamic State jihadists and other extremists from carrying out attacks on Russian soil.
But Russia's intervention has also drawn criticism, with US Secretary of State John Kerry last week expressing concern over a heavy civilian toll in Russian air strikes.