Trump warned late on Tuesday he might end the NAFTA trade treaty with Mexico and Canada after three-way talks failed to bridge deep differences. He also said he may shut down the government if he does not get funding to build a wall on the U.S.-Mexico border.

It was not the first time Trump has threatened to scrap NAFTA. But it was the first time he made the threat since negotiations started, analysts said.

"The strategy of building a wall seems a losing one, even ignoring its moral repugnance," said John Taylor, Jr., president and founder of Taylor Global Vision, a global macro and FX research firm in New York.

"But it will reverberate through the debate on the debt ceiling. We see a shutdown as more likely than the other analysts we have read," he added.

The Congressional Budget Office said in June that Congress would need to raise the debt limit by early to mid-October to avoid a default.

Trump's comments on the border wall and NAFTA came on the heels of his controversial remarks last week about a white supremacist-organized rally in Charlottesville, Virginia that ended in a violent encounter with left-wing counter protesters. Trump had said "both sides" were to blame for the violence.

Taylor said the Charlottesville violence and the criticism of Trump's reaction to it are leading to an increase in pressure on Mexico.

"It is Trump's strategy to stir up white insecurity and aggravate pressure on the people of color - primarily Mexicans in the case of the wall - to solidify his hold on his base," Taylor said.

In late trading, the dollar fell 0.5 percent to 108.97 yen , as the dollar index slid 0.4 percent to 93.151 <.DXY>.

The euro earlier was propped up by strong German and French PMI survey readings, although analysts warned the currency's gains could be short-lived due to concerns about heavy one-sided bets.

The euro rose 0.5 percent to $1.1818 .

The German and French PMI data showed both countries registering strong private-sector growth in August.

Amid President Trump's comments, investors also awaited speeches from Federal Reserve Chair Janet Yellen and European Central Bank President Mario Draghi at the Jackson Hole summit on Friday, though neither was expected to announce new policy messages. In a speech in Germany on Wednesday, Draghi steered clear of market-sensitive comments.

(Reporting by Gertrude Chavez-Dreyfuss; Editing by Meredith Mazzilli and Paul Simao)

By Gertrude Chavez-Dreyfuss