MADRID – Politicians, analysts and ordinary citizens across much of the world welcomed the electoral rebuke given by President Bush’s Republican Party and the resignation of Defense Secretary Donald H. Rumsfeld yesterday.

Against the broad mood of satisfaction, however, there were voices of concern that a power split between Democrats and Republicans in Washington might mean uncertainty in crucial areas like global trade talks.

On Iraq, some worried that Democrats could force a too-rapid retreat, leaving the country and the region in chaos. Others said they doubted the congressional turnover would have a dramatic impact on Iraq policy any time soon, largely because the Democrats have yet to define the course they want to take.

But from Paris to Pakistan, a repeated theme was hope that the Democratic takeover of at least one house of Congress would force Bush to adopt a more conciliatory approach to global crises, and teach a president many see as a “cowboy” a lesson in humility.

“Americans are realizing that you can’t found the politics of a country on patriotic passion and reflexes,” said French schoolteacher Jean-Pierre Charpemtrat.

“You can’t fool everybody all the time – and I think that’s what Bush and his administration are learning today.”

Italian Premier Romano Prodi said Rumsfeld’s surprise resignation underscored the depth of what has happened in America.

“Even though U.S. politics had already started changing, Rumsfeld’s resignation means an accentuation of this change,” Prodi said. “We’ll see over the next few days what the new direction will be. But certainly we have a political structure … deeply different from that of a few days ago.”

In an extraordinary joint statement, more than 200 Socialist members of the European Parliament hailed the American election results as “the beginning of the end of a six-year nightmare for the world.”