The Obama administration’s top diplomat also urged Chinese officials to lower tensions in East Asia and proposed hosting a three-way meeting between the U.S., China and Japan to ease the latest flare-up: competing claims over East China Sea islands, a dispute that has soured ties between Beijing and Tokyo.

She conveyed the messages in a private meeting with Chinese State Councilor Dai Bingguo on Hainan Island just hours after similar talks in Vietnam with Chinese Foreign Minster Yang Jiechi on the sidelines of a summit of regional leaders. The sessions are meant to ease strained U.S.-China ties before a January state visit to the U.S. by Chinese President Hu Jintao.

"It is in all of our interests for China and Japan to have stable and peaceful relations," Clinton told reporters Hanoi, the Vietnamese capital. The U.S., she said, is "more than willing" to host three-ways talks "where we would discuss a range of issues."

"We made very clear that we want the temperature to go down on this issue," said one senior official who sat in on the Clinton-Yang meeting. The official spoke on condition of anonymity to discuss a private diplomatic exchange.

Yang, the official said, told Clinton he would take the suggestion under advisement but made no commitment on whether China would accept U.S. mediation. Japanese officials have said they would welcome a U.S. role if a trilateral meeting was well prepared, the official said.

Later, China responded coolly to the offer. It made clear its unhappiness with comments Clinton made this week and again on Saturday in which she said the islands are covered by a U.S.-Japan mutual defense pact even though Washington takes no position on their ultimate sovereignty.

A statement on the Chinese Foreign Ministry’s website said Yang told her that the United States should act with discretion and make no "wrong remarks" on the sensitive issue of the islands. He also repeated Beijing’s claim to the islands and insisted the U.S. should respect China’s stance.

China is also sparring with its neighbors over control of the strategic and potentially oil-rich Spratly and Paracel islands in the South China Sea, which are claimed by Vietnam and other nations as well as Beijing. The contested islands straddle busy sea lanes that are a crucial conduit for oil and other resources fueling China’s fast-expanding economy.

In Hanoi, Clinton told East Asian leaders that a peaceful resolution of all the maritime disputes is in U.S. national security interests. She called on China to cooperate with the regional bloc that represents the other claimants; China wants to deal with the nations individually.

Clinton came to Hainan, a tropical island east of Vietnam in the South China Sea, at the invitation of Dai, who outranks Yang in Beijing’s government hierarchy. The island is rich with symbolism of China’s growing military might and is home to major Chinese military installations, including naval bases and a massive surveillance facility.

It was on Hainan that a U.S. Navy spy plane was forced to land in April 2001 after colliding with a Chinese fighter jet. China held the 24 U.S. crew members for 11 days until the Bush administration apologized for the collision that killed a Chinese pilot. No U.S. secretary of state had visited the island before.

Clinton also sought to clarify China’s policy on exports of exotic metals that are critical to the global high-tech industry. Recent restrictions on such sales have prompted widespread international concern.

With Yang, at least, she said she had won assurances that China will remain a "reliable supplier" of rare earths, which are needed to produce items such as cell phones, missiles and solar energy panels.

Clinton said Yang told her that "China has no intention of withholding these materials from the market." She added that despite that assurance, the U.S., Japan and Europe would continue to look for other suppliers of rare earths.

China now produces 97 percent of the world’s supply since most of the industrialized world, including the U.S., Japan and Europe, largely abandoned their production in favor of cheaper Chinese exports.

There was no immediate comment from Chinese officials. China said this past week that it would not use the exports of rare earths as a political bargaining chip in its dealings with other countries. Japanese companies have said since the island row erupted last month, China effectively has blocked exports of the minerals.

In her meeting with Yang, Clinton also asked China to use its influence with North Korea to keep the country from taking any provocative actions ahead of an upcoming G-20 summit that South Korea will be hosting next month.