Speaking during a visit to Singapore, Abe said ties between the neighbours are "mutually beneficial" and should be restored to normalcy.
Relations between the two Asian powerhouses have been frayed since September following the latest flare-up of a territorial row over tiny islands in the East China Sea that both nations claim.
"I am looking forward to the day when I can have amicable discussions with the leaders of China, an important neighbouring country for Japan," Abe said in a speech to an academic forum.
Asked after his speech about what he could do to improve Japan's relations with Beijing now that he has tightened his grip on power in the recent upper house elections, Abe said the leaders or the foreign ministers of the two countries should meet.
Such a meeting should be held "as promptly as possible and no preconditions attached".
"We are neighbours and therefore challenges are unavoidable and that is the reason why leaders should meet and try to resolve these," he said.
Four vessels spent three hours in the territorial waters of a Tokyo-controlled archipelago, where they traded warnings with their Japanese counterparts.
The move -- by vessels whose crews were likely to be armed, according to academics -- marks an upping of the ante in the blistering row over ownership of the Senkakus, which Beijing claims and calls the Diaoyus.
It also came the day Japan's defence ministry recommended establishing amphibious units and acquiring surveillance drones to protect outlying islands.
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