President Bush thanked Prime Minister Junichiro Koizumi on Friday night for Japan's $1.5 billion commitment to rebuilding Iraq. But the two men emerged from a meeting and informal dinner here with what appeared to be a muddled message, and no agreement, on the value of the dollar.

That issue is politically critical for both of them at a moment when Japan and the United States are both struggling to revive manufacturing jobs.

Mr. Koizumi announced his decision to make a substantial financial contribution to Iraq in the days before Mr. Bush arrived, so that it did not appear that he was acting under pressure.

On Air Force One, a senior administration official told reporters that Mr. Bush would use his meetings this week with Asian leaders to seek similar contributions, but cautioned that the administration did not expect that many countries would be able to match Japan's contribution and that few would send troops.

Mr. Bush landed in Manila on Saturday for an eight-hour visit that includes a meeting with the Philippine president, Gloria Macapagal Arroyo, and an address to the Phillipine Congress.

Mr. Koizumi, an American official said, made no commitment about whether he would deploy Japanese peacekeeping forces to Iraq. In July, Japan's Parliament authorized sending 1,000 troops, but on Thursday the government said it was still studying the appropriate time and place.

Mr. Koizumi, who is up for re-election on Nov. 9, has tried to keep the issue out of the public eye until after election day.

The senior Bush administration official said it was not clear whether troops from Turkey, whose presence in Iraq has been opposed by the American-appointed Iraqi Governing Council, would ever be deployed.

"The Iraqis are obviously an important party in this," the official said. "I think it's time to just let people try and work it out."

According to Japanese officials, Mr. Koizumi urged Mr. Bush to work more within the United Nations structure, citing the Security Council vote on Thursday on Iraq as an example of how the United States could use the institution "as a bridge" to support its goals in Iraq and the Middle East as a whole.

Mr. Bush, the Japanese officials said, responded by describing the United Nations as an aging and slow institution and made no commitments. American officials, in briefing reporters, made no mention of any discussion of the United Nations.

The leaders met at what was described as a social dinner for Mr. Bush at the Akasaka State Guest House, one of the palaces surrounding the main Imperial Palace in the center of Tokyo. The dinner was a deliberately low-key affair: both men were in open-collared shirts, and they avoided the kind of scene they made 18 months ago when they ate in a crowded Tokyo restaurant.

While they said nothing to reporters, they allowed in photographers to underscore what they describe as a close, informal working relationship.

That is particularly important for Mr. Koizumi, as his party faces elections in a few weeks. He must balance, one Japanese diplomat said Friday night, "a closeness with America and a recognition of the great sensitivity" about deploying Japanese forces to a region where deadly violence is still a daily event.

Polls show Japanese extremely reluctant to put their military in harm's way, though Mr. Koizumi seems intent on avoiding the trouble Japan ran into in 1991, when it sent plenty of money for the Persian Gulf war but no troops.

The consensus between the men broke down when the subject turned to the strength of the dollar, which could become a major political problem for Mr. Bush.

The president is under pressure from American manufacturers, including some of the biggest donors to his campaign, to let the dollar fall in value relative to some major Asian currencies. A weaker dollar would lower the price of American goods abroad, which would help American companies to export more. On the other hand, it would make Japanese and Chinese imports more expensive in the American market.

Mr. Bush clearly wants to accommodate the exporters, but he is also aware of the benefits of a strong dollar for many sectors of the economy. So he has split the difference, saying the United States still favors a strong dollar but wants "the market to determine exchange rates."

That last phrase is a signal to American companies, administration officials say, that Mr. Bush believes that China and Japan should stop intervening in the markets to keep the dollar artificially high.

In short, the new American policy appears internally contradictory. Mr. Bush is declaring that the dollar should be strong, while calling for a freeing of markets that would, most experts guess, send its value down in relation to the Japanese and Chinese currencies.

"It's a combination of statements that make no sense, when you think about it," one senior American official deeply involved in the issue said just before Mr. Bush left Washington on Wednesday. "Either you want a strong dollar or you want the markets to determine the rate, but you can't pray at both altars."

Mr. Koizumi's problem is the mirror image of Mr. Bush's. He wants a strong dollar and a weak yen, to improve Japan's exports.

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