BAGHDAD (Reuters) - Violence in Iraq during Ramadan has fallen by almost 40 percent from last year, the U.S. military said on Sunday, despite a warning from al Qaeda that it would increase attacks during the Muslim holy month.

U.S. military spokesman Rear Admiral Mark Fox said a "surge" of 30,000 extra troops into Iraq this year and the new tactic of moving soldiers into small combat outposts instead of "commuting to the war" from large bases had helped bring down violence.

"We are substantially below last year's level. As a matter of fact, in comparison to this time last year, about 38 percent lower in terms of Ramadan violence levels," he told a news conference, adding that that overall levels were still too high.

Al Qaeda said at the start of Ramadan, more than two weeks ago, that it would escalate attacks and would target tribal leaders who were cooperating with security forces.

Marine Brigadier-General Mark Gurganus, commander of U.S. ground troops in Anbar province in western Iraq, said there had been 76 attacks in the first week of Ramadan in his area of command, and 91 in the second week.

"One year ago, during the same week, we had 415 incidents. The 38 percent reduction across Iraq -- we enjoyed quite a bit sharper," Gurganus said.

Anbar was once the most dangerous province in Iraq for Iraqis and U.S. troops but is now being hailed as one of Iraq's few success stories after U.S. forces helped local Sunni Arab sheikhs organize their young men into tribal police units.

U.S. President George W. Bush cited the progress in Anbar as a validation of his strategy of pouring extra troops into Iraq this year, to buy time for political leaders to make progress on reconciling Iraq's warring Shi'ites and Sunni Arabs.

U.S. commanders have since been working on introducing similar models in other volatile areas around Baghdad, although it has yet to be applied in major urban areas.

Bush told Congress that successes in the unpopular war would allow between 20,000 and 30,000 troops to be withdrawn by July.

The 13th Marine Expeditionary Unit of 2,200 Marines left Iraq this week, the first unit scheduled to depart.

U.S. commanders have tied the withdrawal of their troops to the readiness of Iraqi security forces to assume responsibility.

Fox said logistics support remained the biggest hurdle for Iraqi security forces, while Gurganus said a lack of leadership also had to be addressed before they could take over in Anbar.

"You don't just go out into the street and find an officer," he said.

SPECTACULAR ATTACKS

Fox said the reduction in attacks did not mean that the Sunni Islamist al Qaeda had been "defanged."

Gurganus added: "One of the things that always concerns me is their constant desire to pull off the one spectacular attack."

Iraqi soldiers killed 40 suspected militants during operations in three northern provinces in the volatile provinces of Diyala, Salahuddin and Kirkuk, the Defence Ministry said.

Despite the overall decline attacks during Ramadan, Fox said there had been an "uptick" in the past few days. On Wednesday, 59 people were killed in bomb attacks across Iraq.

The "surge" of extra U.S. and Iraqi troops has also targeted Shi'ite militias, which Washington says are being trained and supplied by Shi'ite Iran.

Tehran denies the charge and blames Iraq's sectarian violence, in which tens of thousands have been killed, on the 2003 U.S.-led invasion to topple Saddam Hussein.

Fox said a raid in Baghdad's Rasheed district had uncovered 36 Iranian-made 107 mm rockets, four of which were "wired and ready to fire."

The commander of U.S. forces in Iraq, General David Petraeus, was quoted by the Los Angeles Times on Sunday as saying that Iraqi Prime Minister Nuri al-Maliki had secured a pledge from Iran's President Mahmoud Ahmadinejad to prevent weapons flowing from Iran to Iraq.

Ahmadinejad said during a recent meeting that he would "stop the flow of weapons, the training, the funding and the directing of these militia extremists that have been such a huge problem, really, for Iraq," the newspaper quoted Petraeus as saying.

(Additional reporting by Dominic Evans in Baghdad)