By Caren Bohan and Susan Cornwell

WASHINGTON, April 13 (Reuters) - Better relations between Washington and Tehran would help Iraq and lessen the tendency of Iran to meddle in the affairs of its neighbor, the Iraqi government spokesman said on Friday.

Ali al-Dabbagh was speaking at a White House news briefing where he supported President George W. Bush's effort to resist a timetable for withdrawing U.S. troops from Iraq and said a premature U.S. pullout would leave a power vacuum.

The Bush administration has repeatedly accused Iran of fueling Sunni-Shi'ite violence in Iraq by providing arms and other support to Shi'ite militias. Iraq's government includes both Sunnis and Shi'ites but is led by Shi'ite Prime Minister Nuri al-Maliki.

"There is an interference from the Iranians in Iraqi affairs, we don't deny that," Dabbagh said. "We feel that the improvement and the better relations between the United States and Iran could minimize -- could make the interference less."

Washington, which has had hostile relations with Tehran's Islamic leaders since the overthrow of the Shah in 1979, is leading international efforts to curb Iran's nuclear program, which it says is aimed at making a bomb. Iran says the program is for energy generation.

Iran is pressing for the release of five Iranians detained in Iraq by U.S. forces and says unless they are freed it may not attend a multilateral conference in Iraq next month.

Echoing a line used by Bush, Dabbagh said it would be a victory for insurgents if U.S. troops left Iraq too early and cited Thursday's bomb attack on the Iraqi parliament to back his case.

"We feel that the premature withdrawal, it would be a great gift for those who did yesterday's attack, and definitely it will make a vacuum of power in Iraq, which is not desirable by anyone," Dabbagh said.

Bush is opposing efforts by the Democratic-led Congress to make passage of a $100 billion bill to fund the war conditional on setting a timetable for a U.S. withdrawal. The president has threatened to veto any bill that contains such a timetable.

Dabbagh said that he hoped that the training of Iraqi forces would allow for a transfer of more responsibility to those troops by the end of the year.

"Then it will open the door for negotiating about the withdrawal of the Americans," he said.

Seeking a compromise on the stand-off over a timetable, Senate Armed Services Committee Chairman Carl Levin, a Michigan Democrat, suggested emphasizing "benchmarks" that push Iraqis to achieve a political settlement.

Senate Minority Leader Mitch McConnell, a Kentucky Republican, indicated he might be open to this. "I wouldn't completely rule out the possibility" of benchmarks, McConnell said. "It would depend on how they were crafted."

Amid talk that some Democratic lawmakers were considering visiting Iran and after a trip by House Speaker Nancy Pelosi to Syria earlier this month, Vice President Dick Cheney urged members of Congress to forego such visits.

"I think we'd all be better off if they'd all stay home and get their work done," Cheney, one of the main figures behind the 2003 invasion of Iraq, told a radio interviewer during a visit to Chicago. (Additional reporting by Richard Cowan)

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