TOKYO — Defense Secretary Donald H. Rumsfeld said Friday guerrillas in Iraq have remained a deadly threat to the technologically superior Americans by studying the way U.S. troops fight. The final test, he said, will be, "Who's going to outlast the other?"

"The remnants of the regime are going to school on us," Rumsfeld told reporters while flying to Tokyo on a six-day Asian trip. After U.S. tactical changes, "They watch what takes place, and then they make adjustments," he said of the shadowy Iraqi opposition.

"The test is who's going to outlast the other, and the answer is we're going to outlast them," the defense secretary said.

In Washington, President Bush said the United States may begin transferring power back to the Iraqi people soon, but American troops will remain in Iraq until the country is free and peaceful. "We will stay there until the job is done," the president said.

However, Secretary of State Colin Powell, in an interview with a Nashville, Tenn., television station, said the number of U.S. troops is likely to be reduced as Iraq builds up its forces.

Bush, in comments after an Oval Office meeting with Italian President Carlo Azeglio Ciampi, defended the U.S. strategy for fighting back against the increasingly deadly insurgency in Iraq with ramped-up bombing and other offensive actions.

"The enemy is changing tactics on the ground, so we're changing our response, and that's what you're beginning to see," Bush said.

Rumsfeld arrived in Japan just after an attack on an Italian compound in Iraq prompted the Japanese, one of America's most steadfast allies, to delay the dispatch of troops to Iraq.

In a news conference at the Japan Defense Agency headquarters Saturday, Rumsfeld said the U.S. government has no problem with the Japanese government taking more time to decide when or if it would send troops.

"We are confident that our friends here will make decisions that are appropriate to them and that is what we want them to do," Rumsfeld said.

Japan Defense Agency chief Shigeru Ishiba said at the news conference that his government "will closely watch the situation" in Iraq before making a final decision. "We would like to do it as soon as possible," he added.

Prime Minister Junichiro Koizumi told Rumsfeld at a meeting Friday that the United States must do more to spread the word that the American cause is Iraq is just.

A Rumsfeld aide who was present at the meeting said Koizumi stressed the importance of making people in Iraq, in the Gulf region and around the world understand the importance of the cause. "And he wanted to think of ways that it could be better understood," the aide said, speaking on condition of anonymity.

He and another senior U.S. official present at the meeting said they did not take the comments as criticism from Koizumi.

Koizumi told Rumsfeld that Japan strongly supported the U.S. role in Iraq, even though it has decided to put off sending troops there, the Rumsfeld aide said.

Rumsfeld met Saturday morning with Foreign Minister Yoriko Kawaguchi. Among the topics they discussed were an impasse over U.S. demands for more legal protections for U.S. troops who are arrested for crimes committed in Japan, according to a senior U.S. official present at the meeting. They agreed the time was right to press for a resolution of the dispute, but they set no timetable for new negotiations.

Japan probably is America's most important ally in Asia, and the Bush administration had hoped the Japanese also would send troops before the end of the year, in addition to the billions in aid they have pledged.

After Wednesday's deadly attack on an Italian compound in south-central Iraq, however, Chief Cabinet Secretary Yasuo Fukuda backed off, saying the security situation in Iraq remains too unstable.

The government in South Korea, where Rumsfeld was headed Monday, also dealt the Pentagon a setback this week by pledging a smaller troop deployment to Iraq than Washington had hoped.

Rumsfeld has said repeatedly that the Bush administration wants countries to contribute troops to Iraq only if they feel it is in their self-interest — and in numbers that suit them.

But the timing of the announcements by Tokyo and Seoul, as Rumsfeld was en route, gave weight to the perception that even the administration's best allies are doubtful of progress in Iraq.

Rumsfeld thanked the Japanese government for pledging $1.5 billion in grants for 2004 and an additional $3.5 billion in loans to help rebuild Iraq over the following three years, his aides said, adding that Koizumi did not mention plans for further steps to help.

Koizumi later told Japan's NHK television network: "We agreed to make every effort to cooperate in the reconstruction and development of democracy in Iraq."

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In the interview with reporters on Rumsfeld's flight from Guam to Tokyo, Rumsfeld showed no sign of disappointment at Japan's decision and even suggested that the U.S.-led coalition in Iraq is gaining strength.

He said he was impressed by Italy's stated determination to remain in Iraq, even after losing 18 people in the attack at Nasiriya. The Italians indicated they may send replacement forces, he said.

"So the signal that's been sent is quite the contrary" to any suggestion that the coalition is in trouble in Iraq, Rumsfeld said.

A total of 32 countries have troops on the ground, and Washington remains in discussions with 14 more on providing either combat or humanitarian troops, the defense secretary said.

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