* U.S., South Korea agree on more joint military drills
* Richardson to visit North but not carrying U.S. message
* North Korea artillery testing spooks markets
* China has unique influence, unique responsibility-U.S.
(Adds Richardson visit, quotes, background)
By Paul Eckert
SEOUL, Dec 8 (Reuters) - The top U.S. military official said Tokyo, Seoul and Washington must build an even stronger alliance in the face of North Korean aggression, while calling on Beijing to show leadership by reining in its ally Pyongyang.
Admiral Mike Mullen, chairman of the U.S. Joint Chiefs of Staff, flew into Seoul on Wednesday where he also agreed with his South Korean counterpart to stage more joint military drills to deter North Korea from attacking again.
"It is my hope that, to the degree possible, these will include participation by your neighbors and partners, in particular the Japanese," he said.
"The goal clearly is to have a deterrent effect, so that all-out war never occurs," he told reporters, without providing details about future joint drills.
While they are allies, relations between Seoul and Tokyo have a legacy of bitterness stemming from Japan's brutal colonial rule of Korea and a dispute over islands.
Mullen said he was encouraged to see South Korea sending observers to this week's U.S.-Japan joint military drill and applauded a trilateral meeting of foreign ministers in Washington.
"I would hope that we would see more trilateral action in the region in the future," he added.
A U.S. aircraft carrier group, the military's ultimate show of strength, has been involved in its recent combined maneuvers with South Korea and Japan. More drills will irritate China, which says they are threatening and bring instability to the region.
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Mullen's trip to South Korea and Japan follows talks in Washington on Monday between Secretary of State Hillary Clinton and her Japanese and South Korean counterparts. All three voiced grave concerns over the North Korean attacks and called on China to use its influence to improve Pyongyang's behavior.
On Tuesday, Beijing hit back at the United States and its Asian allies for their refusal to talk to North Korea, saying dialogue was the only way to calm escalating tension on the divided Korean peninsula.
But Mullen said the Chinese must do more.
"They are a world leader and leaders must lead -- particularly to prevent crises and to prevent the kinds of destabilizing activities that are very evident coming out of the leadership in Pyongyang," he said.
"China has unique influence. Therefore, they bear unique responsibility," Mullen told a news conference in Seoul.
He said the U.S and South Korean militaries would avoid taking steps that would escalate into a conflict on the peninsula.
"The North should not mistake this restraint as a lack of resolve -- nor should they interpret it as willingness to accept continued attacks to go unchallenged," he said.
DIPLOMACY
A series of incidents -- including a deadly artillery attack and revelations of Pyongyang's nuclear advances -- have set off a flurry of diplomatic activity involving Seoul, Washington, Tokyo and Beijing.
New Mexico Governor Bill Richardson, a former U.S. special envoy to North Korea, will travel to Pyongyang next week. He said he hoped to help matters but was going as a private citizen and not carrying any U.S. government message.
"I am not carrying any messages, but I want to be helpful during this volatile period," Richardson said in a statement. "If I can contribute to the easing of tension on the peninsula, the trip will be well worth it."
The State Department also said Richardson was making a private visit but that, as usual, he was expected to talk to U.S. officials before he left and when he returned.
The Washington Post reported Richardson had been invited by top North Korean officials involved in the nuclear program.
The North often sends signals through unofficial visitors. In November, it showed a U.S. nuclear scientist hundreds of centrifuges, a development that strengthens the case that the North may be developing another path to atomic bombs.
Deputy Secretary of State Jim Steinberg will lead a U.S. delegation to China next week to try to persuade Beijing to put more pressure on Pyongyang despite Chinese fears that this may destabilize North Korea, a U.S. official said.
Washington, Seoul and Tokyo have been lukewarm toward Beijing's proposal for emergency talks between the six regional powers, worried that they could be seen as rewarding Pyongyang for its deadly attack on a South Korean island two weeks ago.
TEST FIRING BY NORTH
On Monday, South Korea's military said an unknown number of artillery shells from the North fell on its side of a disputed maritime border off the west coast, adding the firing was most likely part of regular exercises.
The South is also conducting live-fire drills in the area.
"It does not appear to be a matter of great concern," a South Korean military official said. However, jittery markets fell on reports of the artillery firing, but within minutes local shares <.KS11> and the won <KRW=> had recovered their losses.
Markets have mostly ignored Pyongyang's actions in recent years, but analysts say they are now more sensitive to North Korean risk after last month's shelling of a South Korean island and Seoul's pledge to hit back hard if attacked again.
"It has been going in a different way than before qualitatively, therefore, we are seeing it as a risk that we cannot ignore next year," said Goohoon Kwon, an economist with U.S. investment bank Goldman Sachs in Seoul.
The two Koreas frequently conduct drills in the area around the Northern Limit Line off the North's west coast. Pyongyang does not recognize the sea border that was established without its consent after the 1950-1953 Korean war.
(Additional reporting by Jeremy Laurence, Danbee Moon and Kim Yeonhee in Seoul; Writing by Jeremy Laurence; Editing by Stacey Joyce)
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