The statement from China said the two countries had agreed "to prevent the situation from aggravating through dialogue and consultation and establish crisis management mechanisms to avoid contingencies".
Japan has previously called for a "hotline" between Tokyo and Beijing to be used in the event of an "accident" during military exercises, for example.
China's official Xinhua news agency said the agreement was "an encouraging icebreaker that has been painfully overdue". "It has brought the relationship between the world's second and third largest economies back to temperatures above the freezing point. Should it be properly implemented, it will mark a turning point in the trajectory of China-Japan relations."
In an indication of the complexity of the issue, Mr Abe affirmed that there had been no change in Japan's stance on the islands, claimed by China as the Diaoyus.
However, a reduction in tensions between the two countries has been broadly welcomed by Japan.
Akira Sato, Japan's state minister of defence, told The Telegraph: "The Senkaku islands are an inherent part of Japan and China is claiming them. However, China is starting to show signs of softening."
There is a hope that increased communications between the neighbours could eventually lead to cooperation. "Stable relations would not only bring important benefits to both countries but have a significant impact on the peace and prosperity of the whole region," said Minoru Kiuchi, Japan's state minister for foreign affairs.
"Given that Japan and China are neighbours, it is natural that issues should arise but direct dialogue should take place without preconditions and we are seeing that develop in a quiet manner, with several meetings recently."
Professor Yasuhiro Matsuda from the University of Tokyo described a meeting between Mr Xi and Mr Abe as a "golden opportunity" for the whole region.
"Next year is 70th anniversary of the end of the Second World War we should become more positive next year. If relations with China and South Korea continue to be bad it will continue to get worse and will be much more difficult for both sides to ameliorate the relationship.
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Japan and China agree to reduce tensions over Senkaku islands
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