(Adds more Bush quotes)

By Andrew Gray and Matt Spetalnick

AL ASAD AIR BASE, Iraq, Sept 3 (Reuters) - U.S. President George W. Bush said on Monday his top officials in Iraq had told him the present level of security could be maintained with fewer forces if what he called current successes continued.

Bush raised the prospect of a troop drawdown during a visit to a desert air base in restive Anbar province in western Iraq, where he said violence had fallen after local Sunni Arab tribal leaders had turned against al Qaeda militants there.

The president flew to Iraq with his security team to meet with U.S. commander General David Petraeus and Ambassador Ryan Crocker for a final review of the war before a showdown in Congress over troop levels.

"General Petraeus and Ambassador Crocker tell me if the kind of success we are seeing continues, it will be possible to maintain the same level of security with fewer American forces," Bush told reporters travelling with him.

Speaking later about troop levels in an address to hundreds of cheering Marines, Bush said:

"Those decisions will be based on a calm assessment by military commanders on conditions on the ground, not a nervous reaction by Washington politicians to poll results and the media."

Bush is visiting Iraq a week before Petraeus and Crocker testify to Congress on Sept. 10. They will report on the impact of Bush's decision to send an additional 30,000 U.S. soldiers to Iraq, a move that increased force numbers to 160,000.

The White House is required to submit its own report to Congress on the situation in Iraq by Sept. 15.

Bush has signalled that he wants to maintain a troop buildup in Baghdad and Anbar for now, and he cautioned members of Congress not to "jump to conclusions" ahead of the reports from his top officials in Iraq.

The president is under pressure from opposition Democrats and some Republicans who want U.S. troops to start leaving after more than four years of war in which 3,700 American soldiers and tens of thousands of Iraqis have been killed.

He flew secretly to the al Asad Air Base in Anbar, once a Sunni Arab insurgent stronghold but now regarded by the U.S. military as a success story.

Bush also met Shi'ite Prime Minister Nuri al-Maliki, who some Democrats in Congress want replaced because of his inability to push through political benchmarks.

The president urged the Iraqi government to "follow up" on what he termed progress on the security front.

"The military successes are paving the way for the political reconciliation and economic progress that Iraqis need to transform their country," Bush said.

ATTACKS DOWN

The U.S. military says sectarian attacks have fallen since the U.S. reinforcements deployed to give Iraqi leaders the chance to heal the deep sectarian divide between warring majority Shi'ites and Sunni Arabs.

But while some security gains have been achieved, no key laws have been passed, and Maliki's cabinet has been hit by the withdrawal of nearly half his ministers.

Bush was accompanied by Secretary of State Condoleezza Rice and national security adviser Steven Hadley. Defense Secretary Robert Gates arrived separately.

"This is very much the meeting of the war council," Pentagon spokesman Geoff Morrell said before Bush held his talks.

"I would anticipate that after Petraeus and Crocker address the Congress that the president will articulate in some fashion the way forward."

The decision to meet in Anbar is symbolic. Such a trip by Bush would have been unthinkable just months ago, when the province was the most dangerous in Iraq for U.S. troops.

But a rebellion by Sunni Arab tribes against Sunni Islamist al Qaeda has pacified Anbar and will likely be held up as a success of U.S. military strategy when Petraeus addresses Congress in one week.

Bush said the change in Anbar was an example of what could happen in Iraq, noting he had been told last summer that the province was lost.

"Today Anbar is a really different place," he said.

Bush's stopover in Iraq had not been announced in advance. The president, who visited Iraq in June last year and previously in November 2003, was on his way to a meeting of Asia-Pacific leaders in Sydney and was due to spend six hours in Iraq.

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