Japan will never compromise with China in the dispute over a chain of islands in the East China Sea but will make a strong effort to avoid further deterioration of relations with its powerful neighbor, Prime Minister Yoshihiko Noda said.

"As for the Senkakus, they are an inherent part of our territory in light of history and also under international law," Noda told reporters in New York on Wednesday after attending a meeting of the UN General Assembly.

“Therefore, there can’t be any compromise that would be a step back from this position,” Noda said.

Japanese and Chinese foreign ministers reportedly failed to ease bilateral tensions during a meeting in New York late on Tuesday but agreed to keep discussing the issue through diplomatic channels.

"We will make sure that these cases will not affect adversely our bilateral relationship. We shall maintain reason and try to resolve the issues calmly and make sure there is good communication between us," Noda said.

The relations between the two countries have recently plummeted to their worst level in years over a chain of islands claimed by both countries.

The islands, known as the Senkaku to Japan and Diaoyu to China, have been at the center of a dispute recently that has triggered violent anti-Japanese protests across China and caused Japanese companies to suspend operations in China.

The tensions escalated in August, after Japan formally announced its decision to buy three of the five disputed islands from the Kurihara family for 2.05 billion yen ($26.1 million).

The islands, which are also claimed by Taiwan, lie on a vital shipping route and are situated above large hydrocarbon deposits.

Japan claims it has occupied the islands since 1895, while China maintains the islands were recognized as Chinese as early as 1783.