WASHINGTON, May 10 — President Bush offered his first public concession to try to resolve the impasse over Iraq war spending today, as he confronted new pressure from his own party over the conflict and House approval of a plan that would provide money for combat operations only through midsummer.

After a briefing at the Pentagon around midday, Mr. Bush said he had instructed Joshua Bolten, the White House chief of staff, to reach “common ground” with lawmakers of both parties over setting firm goals, or benchmarks, to measure progress in Iraq. Mr. Bush had previously insisted he wanted about $95 billion for the military with no strings attached.

“It makes sense to have benchmarks as a part of our discussion on how to go forward,” Mr. Bush said, even as he threatened to veto the House plan, which was approved on a vote of 221 to 205, to require him to seek approval in two months for the balance of the war money.

Before that vote tonight, House Democrats demonstrated their opposition to continuing the war when 169 of them voted for a separate plan that would have required the withdrawal of American troops to begin in 90 days, with most forces out within another six months.