WASHINGTON — A sharply divided House brushed aside a veto threat yesterday and passed legislation that would order President Bush to begin withdrawing troops from Iraq by October 1.

The 218–208 vote came as the top American commander in Iraq told lawmakers the country remained gripped by violence but was showing some signs of improvement.

Passage puts the bill on track to clear Congress by week’s end and arrive on the president’s desk in coming days as the first binding congressional challenge to Mr. Bush’s handling of the conflict now in its fifth year.

“Our troops are mired in a civil war with no clear enemy and no clear strategy for success,” the House majority leader, Rep. Steny Hoyer, said.

Republicans promised to stand squarely behind the president in rejecting what they called a “surrender date” handed to the enemy.

“Al Qaeda will view this as the day the House of Representatives threw in the towel,” said Rep. Jerry Lewis of California, ranking Republican on the House Appropriations Committee.

The $124.2 billion bill would fund the war, among other things, but demand troop withdrawals begin on October 1 or sooner if the Iraqi government does not meet certain standards. The bill sets a nonbinding goal of completing the troop pull out by April 1, 2008, allowing for forces conducting certain noncombat missions, such as attacking terrorist networks or training Iraqi forces, to remain.

House and Senate appropriators agreed to the legislation earlier this week. The Senate was expected to clear the measure today, sending it to the president.

While Mr. Bush was confident the bill would ultimately fail because Democrats lacked the two-thirds majority needed to override a veto, he kept up pressure on lawmakers. On the same day as the House vote, the president dispatched his Iraq commander, General David Petraeus, and other senior defense officials to Capitol Hill to make his case: Additional forces recently sent to Iraq are yielding mixed results and the strategy needs more time to work.