BERLIN – While Tuesday’s mandate gave President Bush all the congressional support he needs to pursue the Iraq war, European backing won’t increase, and may sharply decrease, in his second term.

As the election’s results were made known, European leaders spoke of the importance of working with President Bush and an American alliance. But they made it clear that the election didn’t change their attitudes toward the war.

“We have made our position clear throughout the campaign, and it is unchanged: Germany will not be sending troops to Iraq,” a German Foreign Ministry representative said.

There was also bad news for Bush from supporters. Hungary announced on Election Day that its 300 troops will be out of Iraq by the end of March. Others aren’t far behind. In Ukraine, both presidential candidates have pledged to withdraw troops in early 2005. Polish officials have announced that their troops will leave after January’s parliamentary elections in Iraq.

According to European news reports, the Netherlands, Bulgaria and Romania are discussing getting their troops out next year, limiting the European presence to Italy and Great Britain.

While the European nations in question represent fewer than 7,000 troops, compared with the 142,000 the United States has in Iraq, withdrawing those troops would damage the U.S.-led military coalition’s international feel.

Otfried Nassauer, the director of the influential Berlin Information Center on Trans-Atlantic Security, said he doubted that European leaders would consider deeper involvement in Iraq unless the United States boosted its own troop presence and ceded control to an Iraqi government and the United Nations.

“Relations with Europe in his second term may well be more difficult than during the first term,” Nassauer said. “International policy made under the law of the strongest wins is never favored by those who are not the strongest. If he continues along the path on which he started, the United States will soon be alone in Iraq.”

Dick Leurdijk, a senior fellow with the Clingendael Institute, a research center in the Hague, Netherlands, said the desperation of the situation in Iraq could force Bush to change his approach to the war, and that could lead to European nations becoming involved.

“The U.S. cannot leave under the current conditions, needs an exit strategy, and that is not possible without the Europeans,” he said. “He needs support from somewhere if the United States is ever going to get out, and the inescapable conclusion is that it will have to come from Europe.”