By Susan Cornwell

WASHINGTON, Sept 18 (Reuters) - The tug-of-war over Iraq policy intensified in the U.S. Congress on Tuesday, as Democrats renewed their efforts to step up troop withdrawals while an influential Republican senator offered a compromise.

A week after Iraq commander Gen. David Petraeus announced gradual troop reductions in Iraq through next summer, Senate Democrats seeking a faster pullout pledged to hold a vote soon on a proposal they think is their best chance to influence the course of the war.

Sen. James Webb, a Virginia Democrat, is proposing that U.S. troops should spend as much time at home as they did abroad on their previous tour of duty in Iraq or Afghanistan.

It is just one of several initiatives on Capitol Hill aimed at pressing President George W. Bush into changing his war strategy and Petraeus' report seems to have done nothing to discourage their proliferation.

Ohio's Republican Sen. George Voinovich, a member of the Senate Foreign Relations Committee, announced a possible compromise plan that would not set a deadline for the end of the Iraq mission, as many Democrats want, but it would not leave it open-ended either.

The plan would enshrine the troop withdrawals already announced, but would also require the Bush administration to report to Congress with a timeline for further reductions.

"We're looking for a comprehensive plan. Right now it's too open ended (in Iraq)," said Voinovich, one of about a dozen Senate Republicans considered swing voters on Iraq policy who are being courted by both parties.

Gordon Johndroe, spokesman for the White House National Security Council, said Voinovich's proposal was being reviewed.

"The proliferation of proposals suggests to me that there's a lot of interest in finding a new way forward in Iraq," said Sen. Susan Collins, a Maine Republican who has been seeking support for her own compromise plan to change the mission in Iraq, together with Democratic Sen. Ben Nelson of Nebraska.

Others were uncertain. "Is it going to build (support) or split and divide and reach no resolution?" asked Sen. Olympia Snowe, also of Maine and one of a few Republicans who has joined Democrats in votes to bring troops home.

"I know where I am, but a lot of people don't," she said.

The Senate has scheduled a vote for Wednesday on whether to consider restoring some legal rights to Guantanamo detainees. A vote on the Webb plan to give troops more rest between deployments should follow this week or next, Democrats said.

Then they plan to return to votes on troop pullouts by bringing up a proposal by Michigan Sen. Carl Levin that would withdraw combat troops within a year of enactment. The proposal has failed to pass before.

Democrats discussed converting Levin's withdrawal deadline to a goal to try to attract more Republican votes. But Senate Majority Leader Harry Reid said they didn't do so because "We haven't found much movement in the Republicans."

Republican critics see the Webb proposal as a back-door way of forcing more withdrawals. The Pentagon opposes the idea, and in July the plan fell short of 60 votes needed to scale procedural hurdles in the closely divided Senate.

Democrats now hope to lure enough Republicans concerned about the repeated tours of duty faced by many U.S. troops to get Webb's plan through. A similar bill has passed the House.

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