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, downplaying 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, downplayed 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 U.S. State Department 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 remains a major issue in the U.S. presidential campaign.

The Pentagon has 146,000 troops there. 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 in Washington)

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