Ties between Asia's two largest economies have long been overshadowed by arguments over their painful wartime history and a territorial spat in the East China Sea, among other issues.
Beijing has also accused Tokyo of interfering in the South China Sea, where China and several Southeast Asian nations are embroiled in an argument over ownership.
Japanese Prime Minister Shinzo Abe will attend the summit, which starts next weekend, along with other world leaders including US President Barack Obama.
Chinese state councillor Yang Jiechi, who outranks the foreign minister, told the head of Japan's National Security Council, Shotaro Yachi, that Japan should "play a constructive role" at the G20 summit, state news agency Xinhua reported late on Thursday.
"The improvement of China-Japan ties has been continuously disturbed by various problems, especially the issues related to East China Sea and South China Sea, which is in the interests of neither side," Xinhua paraphrased Yang as saying.
Yachi also met Chinese Premier Li Keqiang. "The China-Japan relationship is still very fragile although there is a momentum of improvement," Li said, according to Xinhua.
Li said he hoped Japan would adopt a "correct understanding of China and fulfil the commitment to taking Chinas development as its opportunity".
Editor: Ade P Marboen
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