"I want to seize on an opportune time to exchange views" with them, he told reporters before leaving for the Asia-Pacific Economic Cooperation (APEC) summit in Bali on Monday and Tuesday.
"I want to send a message that the door of dialogue is always open."
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But Abe, a conservative hawk, had a handshake and a five-minute chat with Chinese President Xi Jinping on the sidelines of a Group of 20 summit in Saint Petersburg in early September.
The meeting was the first between leaders of the two countries since relations took a nosedive a year ago over the ownership of uninhabited islands, a row that has led to warnings of a possible armed confrontation.
Abe also had a brief stand-up chat with South Korean President Park Geun-Hye in the Russian city during the G20 gathering.
But Japanese media reports said last week that Abe's hoped-for talks with Xi and Park in Bali might not materialise due to reluctance on the part of China and South Korea.
While in Indonesia, the Japanese premier will also take part in top-level talks on the proposed Trans-Pacific Partnership (TPP) free trade pact involving 12 countries, including Japan, the United States and Australia.
US President Barack Obama has shelved his visit to APEC and to an East Asia summit in Brunei later this week , blaming the crisis at home over the US government shutdown.
"It is very unfortunate that President Obama cannot attend it," Abe said adding he would make an "active contribution to help the (TPP) discussions move in a favourable direction toward a conclusion by the end of the year".
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