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By Dean Yates

BAGHDAD, Sept 7 (Reuters) - Seven U.S. troops have been killed in Iraq, including four in the western province of Anbar, where gains in security were hailed this week by U.S. President George W. Bush during an unannounced visit to the desert region.

The U.S. military said on Friday that four Marines were killed in the vast province on Thursday while conducting combat operations. It gave no further details on one of the deadliest days for troops in Anbar in months.

The military also said three soldiers were killed in the northern province of Nineveh on Thursday when an explosion hit their vehicle.

The deaths take to more than 3,750 the number of U.S. soldiers killed since the start of the U.S.-led invasion in 2003. Eighteen U.S. soldiers have died so far this month.

Bush visited Anbar on Monday and said improved security there was an example of what could happen elsewhere in Iraq.

From 2003 until last year, Anbar was the heartland of the Sunni Arab insurgency and the most dangerous part of Iraq.

But a rebellion by Sunni Arab tribal leaders against Sunni Islamist al Qaeda, which once controlled large swathes of the region, has sharply reduced levels of violence.

U.S. forces killed three insurgents and arrested 18 others in raids against al Qaeda in central and northern Iraq on Thursday and Friday, the military added.

The U.S. commander in Iraq, General David Petraeus, will likely highlight the success in pacifying Anbar when he presents a long-awaited report to Congress early next week on Bush's decision to send 30,000 extra troops to Baghdad and Anbar.

The testimony by Petraeus and U.S. Ambassador Ryan Crocker will be vital to any decision Bush takes on troop levels in the face of demands from opposition Democrats and some senior Republicans for U.S. forces to start leaving Iraq.

SECTARIAN DIVISIONS

Petraeus and Crocker are expected to highlight improved security but criticise Iraq's politicians for failing to pass laws seen as vital to healing sectarian divisions between warring majority Shi'ites and Sunni Arabs.

In Sydney for a meeting of Asia-Pacific leaders this week, Bush said he saw signs of progress in Iraq and held out the possibility of a cut in troop numbers from the current 168,000.

The New York Times reported Petraeus had told Bush he wanted to maintain higher troop levels well into next year but could accept a pullback of some 4,000 troops beginning in January.

Petraeus wanted to reduce the risk of military setbacks but his recommendation might satisfy some critics in Congress, the newspaper said, citing senior administration and military officials.

Petraeus "is worried about risk, and all things being equal he'd like to keep as much as he could for as long as he could", a senior military officer told the Times.

In his report, Petraeus will discuss the possibility of far deeper withdrawals, over a period of months beyond January, that could bring levels down to about 130,000 troops, the newspaper reported, citing officials helping prepare the testimony.

More than two thirds of people around the world think U.S.-led forces should pull out within a year, according to a poll published on Friday by the BBC's international service.

The BBC World Service poll, which questioned 23,000 people in 22 countries, found only a quarter of respondents thought foreign troops should stay in Iraq until security improved.

Almost two thirds (61 percent) of Americans who were asked said they thought their forces should leave Iraq within a year, with 24 percent saying they should get out immediately.

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