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FORT LEWIS, Wash., July 8 (Reuters) - U.S. Defense Secretary Robert Gates said on Tuesday he expected to pull more U.S. troops from Iraq as local security forces improve, playing down calls from Baghdad for a firm withdrawal deadline.

"As the Iraqi security forces get stronger and get better then we would be able to continue drawing down our troops in the future," Gates told reporters during a visit to the Fort Lewis Army base in Washington state.

The Pentagon chief stressed any decision to withdraw would be based on the ability of Iraqi troops to take responsibility for security and combat.

"This transition of control and primary responsibility for security is a process that is well under way and, based on everything I've heard, we will be able to continue," he said. "However, that really depends on the situation on the ground."

Iraq, however, has begun to call for a timetable that would set dates for the withdrawal of foreign forces.

Iraqi officials said the timetable should be included in the agreement being negotiated with Washington that will provide a legal basis for U.S. troops to operate when a U.N. mandate expires at the end of the year.

Iraq's national security adviser, Mowaffaq al-Rubaie, on Tuesday said Iraq would not accept any security agreement with the United States unless it included dates for withdrawing troops.

That followed comments from Iraqi Prime Minister Nuri al-Maliki that for the first time suggested a timetable be set under the agreement. He referred to the agreement as a memorandum of understanding, rather than the longer-term "Status of Forces Agreement" Washington seeks.

The State Department, responsible for negotiating the agreement with Iraq, also played down apparent differences with Baghdad.

"The U.S. government and the government of Iraq are in agreement that we, the U.S. government, we want to withdraw, we will withdraw. However, that decision will be conditions-based," said spokesman Gonzalo Gallegos.

Washington was looking for an agreement "that satisfies both our needs," Gallegos said. He said he would not discuss details of the agreement while negotiations continue, nor was he willing to discuss a timetable for completion.

The Iraq war and troop levels remain a major issue in the U.S. presidential campaign. Implementation of any agreement reached between Washington and Baghdad will fall to the next president, who will enter office in January.

Republican candidate John McCain has said he will pull troops out of Iraq as security conditions allow -- in line with the Bush administration's strategy. Democrat Barack Obama promised to withdraw all troops within 16 months, although many experts expect him to back away from that pledge if elected.

Democrats in Congress have tried and failed to attach timelines for withdrawal to war-related legislation. They renewed their call after Maliki's comments, saying a deadline will force Iraqis to take more responsibility.

"He (Maliki) is on the right track," said Assistant Senate Democratic Leader Dick Durbin, an Illinois Democrat. "I hope President Bush and Senator McCain are listening."

The Pentagon has 146,000 troops in Iraq. That force level should drop to about 140,000 by the end of July under a planned reduction. Commanders will then assess security conditions before recommending further troop cuts. (Reporting by Daisuke Wakabayashi at Fort Lewis and Susan Cornwell and David Morgan in Washington, editing by Jackie Frank)

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