“This debate will go on,” promised Speaker Nancy Pelosi of California, who voted against the war spending and described the new benchmarks as token restrictions.

Democrats also pointed to the $2.10-a-hour increase in the minimum wage that was approved as part of the legislation, as well as the extra spending they wrested from the White House for veterans and military health care, Gulf Coast hurricane recovery, farm aid and children’s health care.

While many Democrats joined Ms. Pelosi in dismissing the new benchmarks as inconsequential since the penalties can be waived by the president, the bipartisan authors of the plan say the conditions and the new reporting requirements were significant and could force a serious review of administration strategy as early as July.

“This legislation will not only ensure that our troops get the funding that they need for training, for equipment, for other essential purposes, this legislation is also about accountability and consequences,” said Senator Susan Collins, Republican of Maine, a co-author of the approach written chiefly by Senator John W. Warner, Republican of Virginia.

But to many House Democrats, the new conditions fell far short and represented a failure by their party to fulfill the promise of their winning control of Congress in November. “The American people voted us into power for one reason,” said Representative Lynn Woolsey, Democrat of California. “They trusted us to hold this administration accountable and to bring our troops home.”

The fight over the money began in earnest on Feb. 5 when Mr. Bush requested the Pentagon financing and urged Democrats to deliver a clean bill without restrictions. But Democrats, empowered by their election gains, sought to use the “power of the purse” to push Mr. Bush toward withdrawing combat troops from Iraq. The first spending measure approved last month would have ordered troop withdrawals beginning Oct. 1, but Mr. Bush vetoed that measure on May 1 — the fourth anniversary of his speech aboard an aircraft carrier before a banner declaring Mission Accomplished.

The House then passed a bill that would have provided the Pentagon money in stages, requiring more votes for future installments. That approach went nowhere in the Senate and Democrats and the White House entered negotiations that produced the legislation being considered in the hours before Congress left town for a Memorial Day break.