Abe rejected a recent appeal on Friday from China which said that it was ready for dialogue if Japan acknowledged that a set of islands known as the Senkakus in Japanese and the Diaoyus in Chinese were disputed. (Agencies)
"The Senkakus are an inherent part of the territory of Japan in light of historical facts and based upon international law and the islands are under the valid control of Japan," Abe told reporters in New York after taking part in the UN General Assembly.
"To our regret, incursions by Chinese government vessels in our territorial waters are continuing. But Japan will not make a concession on our territorial sovereignty," he said.
Abe, however, said that Japan sought calm and did not intend to escalate this issue any further.
He called for cooperation with China, saying that the relationship between Asia's two largest economies was critical for the region's security.
"The door to dialogue is always open and I really hope that the Chinese side would take a similar attitude and mindset," Abe said.
Chinese Foreign Minister Wang Yi, speaking ahead of the UN General Assembly, said that he supported talks but that Japan first had to declare that the islands are disputed.
"The whole world knows that there is a dispute," Wang said at the Brookings Institution in Washington last week.
In a speech yesterday to the UN General Assembly, Wang said that China was open to talks on territorial disputes but would also "firmly safeguard" its sovereignty.
"We sincerely hope to properly resolve them through negotiation and consultation with countries directly resolved," Wang said.
"Those disputes that cannot be resolved now can be shelved for future resolution," he said.
Abe, a conservative who is the politically strongest Japanese leader in nearly a decade, has stepped up defence spending and advocated a firm line with China.
In an earlier speech to the Hudson Institute in New York, Abe said officially pacifist Japan should no longer be a "weak link" in global security nor for its ally the United States.
Japanese officials have voiced alarm at the rising number of Chinese ships that have approached the waters, charging that Beijing is using intimidation to challenge
Abe rejected a recent appeal on Friday from China which said that it was ready for dialogue if Japan acknowledged that a set of islands known as the Senkakus in Japanese and the Diaoyus in Chinese were disputed.