(Clarifies status of islands from 1945-72, paragraph seven)
* China's foreign minister says Japan 'stole' islands
* China envoy says Japan committed 'money laundering'
* Japan says no evidence the islands belonged to China
By Paul Eckert and Chris Buckley
NEW YORK/BEIJING, Sept 27 (Reuters) - U.S. Secretary of State Hillary Clinton has urged China and Japan to let "cool heads" prevail in a dispute over a cluster of East China Sea islands, but her pleas fell on deaf ears as Chinese and Japanese diplomats again traded fierce words.
Clinton met Chinese Foreign Minister Yang Jiechi on the sidelines of this week's U.N. General Assembly meeting in New York and said it was important to cool the quarrel over the islands that has soured ties between Asia's two largest economies, a senior State Department official said.
The uninhabited islets, whose nearby waters are thought to hold potentially rich natural gas reserves, are known as the Diaoyu islands in China and the Senkaku islands in Japan.
"The secretary ... again urged that cooler heads prevail, that Japan and China engage in dialogue to calm the waters," the official told reporters.
"We believe that Japan and China have the resources, have the restraint, have the ability to work on this directly and take tensions down, and that is our message to both sides."
Yang, however, used a portion of China's annual address to the General Assembly on Thursday night to forcefully restate Beijing's stance that the islands had belonged to China from ancient times and were seized in 1895 after Japan defeated the Qing Dynasty in a war.
The islands were put under Japan's control in 1895, included under the post-World War Two U.S. military occupation of Japan's Okinawa from 1945-72 and then returned to Tokyo by U.S. authorities in a decision China and Taiwan later contested.
Yang also condemned the Japanese government's purchase of the islands earlier this month from their private owner, a step that sparked protests across China and prompted Beijing to curb bilateral trade and tourism.
"The moves taken by Japan are totally illegal and invalid," he said of the purchase, which Tokyo says was done to ease the dispute by preventing the islands' use by Japanese activists.
"They can in no way change the historical fact that Japan stole the Diaoyu and affiliated islands and that China has sovereignty over them," Yang told the General Assembly.
Japan restated Tokyo's position that no sovereignty dispute exists and that Japan began surveying the islands a decade before deciding to incorporate them in 1895, and there exists no evidence that the islands belonged to China.
"It has only been since the 1970s that the government of China and the Taiwanese authorities began making their assertions on territorial sovereignty over the Senkaku Islands," said Kazuo Kodama, Japan's deputy U.N. ambassador.
"Before then they did not express any objections."
China has declared the islands "sacred territory," and Taiwan has also asserted its own sovereignty over the area.
China's U.N. Ambassador Li Baodong accused the Japanese envoy of "resorting to spurious, fallacious arguments that defy all reason and logic".
"The recent so-called purchase of the islands is nothing different than money laundering," he said, accusing Tokyo of buying stolen property when it acquired the islands this month.
Continuing the barrage of rhetoric on Friday, Assistant Foreign Minister Le Yucheng told a forum in Beijing on the 40th anniversary of China-Japan diplomatic ties that the island purchase decision was "like lobbing an atom bomb at China".
"If Japan continues to act erroneously despite advice to the contrary and keeps going down the wrong path, then Sino-Japanese relations could sink like the Titanic," Le said, according to a transcript of his remarks carried on the ministry's website (www.mfa.gov.cn).
Both China and Japan have sent patrol boats in a game of cat-and-mouse in the waters near the disputed islands, raising concerns that an unintended collision or other incident could escalate into a broader clash.
In a further sign of economic fallout from the dispute, Chinese buyers and Japanese sellers of refined copper have postponed agreement on terms for 2013 shipments.
Chinese and Japanese companies failed to reach a deal in talks this week, even though Japanese sellers were willing to cut price premiums by about 10 percent from last year, a Chinese executive familiar with the talks said. (Editing by Jeremy Laurence)