(Recasts with Democrats comments) By Andrew Gray and Richard Cowan WASHINGTON, Feb 27 (Reuters) - A plan to impose conditions on U.S. troops ordered to Iraq would damage their ability to fight, the top America military officer warned on Tuesday, while congressional Democrats considered a possible alternative. At a meeting of Democrats in the House of Representatives, a proposal was floated to give President George W. Bush some flexibility with the conditions in his push to send 21,500 more troops to Iraq. It was unclear if a majority of Democrats would embrace the proposal, but under the plan Bush would be permitted to sign a waiver on a demand that all troops be properly trained, equipped and rested, said Rep. Chet Edwards, a moderate Texas Democrat. "I think it's responsible to put in waivers that would require the president to take responsibility for troops not being trained or not having been back home for a year before returning to Iraq," Edwards said. "At the same time, it gives him the flexibility if that is needed." Edwards serves on the House Appropriations Committee, which is considering a request by Bush for another $100 billion to wage war in Iraq and Afghanistan. Democrats won control of Congress in November elections largely because of the increasingly unpopular Iraq war. They now face pressure to end the conflict. Rep. John Murtha, a Pennsylvania Democrat, has proposed forcing the Pentagon to certify that troops sent to Iraq are fully trained and equipped and have at least one year between combat deployments. But Marine Gen. Peter Pace, chairman of the joint chiefs of staff, said the conditions pushed by Democrats would cut the number of U.S. combat troops in Iraq and "leave gaps on the battlefield." 'ENORMOUS EFFECT' Democratic leaders said they were not trying to create new conditions, but just demanding the administration adhere to existing military policies. "If those are the rules, then instead of being able to have the 20 brigades on the ground in Iraq that we require ... we would have somewhere between 14 brigades and 19 brigades at most," Pace told the Senate Appropriations Committee. "It would have enormous effect on the battlefield with regard to what is required and what is available." A brigade normally has 3,000 to 5,000 soldiers. There are now nearly 140,000 U.S. forces in Iraq. Murtha has yet to flesh out details of his proposal and it is also unclear how much support it commands in Congress, but Republican leaders have denounced it as a "slow bleed" losing strategy. Military commanders at the Pentagon said the extra 21,500 troops being sent to Iraq will be prepared. "Our deploying units will be manned, trained and equipped and they will be ready for their specified missions," Maj. Gen. Richard Formica, the U.S. Army's director of force management, told reporters. "Well, we'll see," replied House Speaker Nancy Pelosi, a California Democrat. "But there are two other points. How long have they been home ... and how long will they have to stay." House Majority Leader Steny Hoyer, a Maryland Democrat, said, "The American public clearly voted for a new direction, and they voted for a Congress that is engaged and involved in setting policy." "We're going to support our troops but we are also going to urge the administration to abandon failed policies," he said. (Additional reporting by Thomas Ferraro)