A year of heated arguments have prevented the three from holding any top-level meetings, with Beijing and Seoul accusing Abe of showing a lack of remorse for World War II wrongs.
"We should hold a summit meeting and have a frank discussion," Abe said in an interview on public broadcaster NHK, two days after Japan's foreign minister called for similar talks.
Abe, China's President Xi Jinping and South Korean President Park Geun-Hye all came to power around a year ago, but entrenched positions and growing nationalism in the three countries have prevented them from getting together.
China and South Korea see the Yasukuni shrine as a symbol of Japan's wartime aggression in Asia.
Today, Abe reiterated he had visited to make a pledge against war, and like other leaders around the world to pray for those who lost their lives for their countries.
"I want people to think about whether this is wrong. If they think about it, I think the misunderstanding will go away," he said.
Two separate territorial disputes over uninhabited islands in the East China Sea, which Beijing and Seoul say have their roots in Japan's early imperial ambitions, have also roiled relations.
"It would be unreasonable if Japan must clear hurdles for summit talks," he said.
On Friday, Japanese Foreign Minister Fumio Kishida said the respective leaders should "make efforts to solve" their disputes.
The call came after Japan brushed off comments by China's envoy to the African Union in which he branded Abe a "troublemaker".
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