WASHINGTON (AP) - Republicans increasingly are backing a new approach in the Iraq war that could become the party's mantra come September. It would mean narrowly limited missions for U.S. troops in Iraq but let President Bush decide when troops should leave.

So far, the idea has not attracted the attention of Democratic leaders. They are under substantial pressure by anti-war groups to consider only legislation that orders troops from Iraq.

But the GOP approach quickly is becoming the attractive alternative for Republican lawmakers who want to challenge Bush on the unpopular war without backtracking from their past assertions that it would be disastrous to set deadlines for troop withdrawals.

"This is a necessary adjustment in the national debate to reintroduce bipartisanship, to stop the 'gotcha' politics that are going on that seem to be driven by fringes on both sides and change the terms of the discussion," said Rep. Phil English, R-Pa.

English is among the more than 40 Republicans in the House and Senate who are sponsoring legislation intended to shift the mission of U.S. troops. Several other GOP lawmakers, facing tight elections next year and a strong anti-war sentiment in their districts, say they are considering this approach.

"Settling Sunni-Shiite rivalries over who occupies what street in Baghdad is not in the vital interest of the United States," said Rep. Heather Wilson, R-N.M., who said she is considering her options. "And we should only have Americans in harms' way where there are U.S. interests at stake."

Bush's top military commander in Iraq, Gen. David Petraeus, is expected to tell Congress in September that more time is needed to determine whether a massive U.S.-led security push initiated in January is working.

The message is unlikely to be well received on Capitol Hill. Democrats have criticized the strategy as escalating a failing war; Republicans say they want to see progress made by fall.

GOP support has proved crucial to Bush in stalling anti-war proposals in the Democratic-run Congress. Legislation ordering U.S. troops out of Iraq has passed repeatedly in the House only to sink in the Senate, where Republicans threaten a filibuster and Democrats fall short of the 60 votes needed to cut off debate.

House Democrats plan to try again this week with a bill that would begin a pullout this fall. Republicans are expected to overwhelmingly oppose it.

If Bush cannot convince GOP lawmakers by September that he is on the right track, more Republicans are expected to demand change.

But many of them, long on record as opposing an end date for combat, say it makes sense to focus on the mission instead. Yet this approach would amount to a de facto mandate for troop withdrawals because of the large number of forces assigned to combat missions.

The goal, they say, is to end the U.S.-led daily patrols in the streets of Baghdad and restrict troops to fighting al-Qaida terrorists and training Iraq security forces.

"If you do that you've greatly reduced the loss of life, which is what matters most," said Rep. Mike Castle, R-Del.

The idea of forcing such a change gained prominence last December when the Iraq Study Group concluded Bush should do more to hand over the combat mission to Iraqi forces.

The bipartisan commission envisioned an ambitious and new diplomatic push, with U.S. troops remaining in the region primarily to supply and train the Iraqi army and to target terrorist cells.

Since then, some 40 Republicans and 31 Democrats have signed on to legislation by Rep. Mark Udall, D-Colo., and Sen. Ken Salazar, D-Colo., that urges Bush to embrace the commission's recommendations.

A much smaller, though growing number of Republicans supports requiring that Bush submit to Congress a detailed, new military strategy to change the mission of U.S. troops.

In the past week, Castle and English agreed to co-sponsor the legislation by Democratic Reps. Neil Abercrombie of Hawaii and John Tanner of Tennessee.

Sens. John Warner, R-Va., and Richard Lugar, R-Ind., have proposed similar legislation.

Sen. Susan Collins, R-Maine, a co-sponsor of Salazar's legislation on the Iraq Study Group, wants to go further: binding legislation that would order Bush to restrict the mission of U.S. troops to counterterrorism, training Iraqis and protecting U.S. assets.

The goal, she says, is to "set the stage for a significant but responsible withdrawal of American combat troops over the next year."

For most of these lawmakers, their decision to embrace change is colored by politics.

Collins is seen by Democratic challengers as particularly vulnerable in the 2008 elections because of the overwhelmingly anti-war sentiment among Maine voters.

English faces an anti-war, anti-incumbent sentiment among Pennsylvania voters, who in 2006 ousted four GOP House members and Republican Sen. Rick Santorum.

Wilson's fellow Republican from New Mexico, Sen. Pete Domenici, recently broke with Bush on Iraq and embraced Salazar's proposal.

Castle was among a dozen lawmakers challenged in an ad campaign in May featuring three retired generals saying politicians cannot expect to win re-election if they support Bush's Iraq policy.