China and Japan "need each other", Japanese Prime Minister Shinzo Abe said on Tuesday as he called for the testy Asian neighbours to step up tentative efforts to put deep hostility behind them.

"Japan and China, we need each other. We are in a way inseparably bound with each other," Abe told reporters in Beijing after an Asia-Pacific summit.

"Japan and China both have responsibility for peace and prosperity of the region and of the world."

Beijing and Tokyo's historically frosty relations have plunged to their lowest in decades over competing claims to Japanese-controlled islets in the East China Sea, and Tokyo's 20th-century history of aggression.

But Chinese President Xi Jinping met with Abe on Monday in Beijing on the sidelines of the Asia-Pacific Economic Cooperation (APEC) summit hosted this year by China.

The rare encounter -- the first by leaders of the world's second- and third-largest economies in three years -- has raised hopes of a possible thaw.

Abe said the two sides "hope to conduct several dialogues" but did not offer specifics when asked when another summit might occur.

"Many countries of the world are expecting to see an improvement of the relationship between Japan and China," Abe said.

"Many leaders have told me they are delighted that the summit has taken place."

- Stiff meetings -

China and Japan are closely linked economically, but political tensions have endured between Asia's two heavyweights for decades, stemming largely from lingering anger over Japan's brutal World War II invasion of its neighbour.

At the same time China's Communist authorities stoke a narrative of historical victimhood to appeal to nationalist sentiment and bolster their claim to a right to rule.

China's neighbours also are wary of its rise, especially Beijing's increasingly uncompromising moves to assert its disputed sovereignty claims in the East China Sea and South China Sea.

Relations with Japan plunged in 2012 when Tokyo nationalised part of the Senkaku islands, an uninhabited chain in the East China Sea.

China, which claims the islands under the name Diaoyus, accused Japan of upsetting a delicate equilibrium that had held for decades. Japan has refused even to acknowledge the existence of competing claims.

The way was paved for the Xi-Abe meeting by a framework agreement announcement on Friday in which each side pledged efforts to prevent the situation spinning out of control.

Their statements on the issue, however, were finely worded, allowing both to spin developments as a victory on their own terms.

The encounters between the men during formal APEC events were also notable for their stiffness.

The meeting on Monday appeared strained, with footage of the two leaders' initial handshake showing them looking deadpan and Xi not responding to Abe's greetings.

Abe told Japanese media afterwards that he had asked Xi to establish a hotline aimed at preventing clashes at sea.

But two Japanese officials told AFP that during the 30 minutes of talks, the leaders mentioned neither the islands nor the Yasukuni shrine, a spot reviled by Japan's neighbours as a symbol of the country's militarist past.

Abe's visit to the shrine in December last year infuriated Beijing and Seoul, who say the inclusion of senior war criminals among those honoured by the site makes it an insult to the grievous injuries Tokyo inflicted up to and during World War II.

China's state-run media quoted Xi telling Abe during their meeting that "severe difficulties" had emerged in their relationship and that "the rights and wrongs behind them are crystal clear".

The report did not elaborate.

Earlier Tuesday, the United States welcomed the Xi-Abe meeting.

"We welcome the meeting yesterday between President Xi and PM Abe. It's an opportunity to reduce the tensions between the two countries," deputy national security advisor Ben Rhodes told reporters in Beijing.

Historical and regional disputes have strained Abe's relationship with not only Xi but also South Korean President Park Geun-Hye, who has rebuffed the Japanese leader's requests for a formal one-on-one meeting.

Ties between the two remain frosty amid a territorial row over a tiny batch of rocky islets and Seoul's demands for further reparations for so-called "comfort women" who were forced to work as sex slaves in Japanese World War II military brothels.

One small breakthrough appeared to take place Monday night, according to Abe: the Japanese leader said he happened to be seated next to Park at the APEC opening dinner due to the alphabetical seating by country, and so "very naturally, we began a conversation".

"In a way, we were able to exchange extremely candid views," Abe said, citing agreement between the two on facilitating progress on the US-favoured Trans-Pacific Partnership (TPP) trade pact.