The US president told marines at al-Asad air base: “Anbar is a huge province. It was once written off as lost. It is now one of the safest places in Iraq.”
However, David Isenberg, a national security expert based in Washington, said: “Any place can be saved temporarily if you pump enough troops into it.
“Anbar province has had a reduction in violence but that has very little to do with the ‘surge’.”
Bush said any troop reduction would be based on “a calm assessment by our military commanders on the conditions on the ground” and “made from a position of strength”.
‘No rule of law’
It would not be “a nervous reaction by Washington politicians to poll results in the media”.
At the air base, Bush also held what he called “good, frank” talks with leaders of Iraq’s Shia Muslim, Sunni Arab and Kurdish communities, including Nuri al-Maliki, the prime minister, and Jalal Talabani, the president.
Bush’s trip to Iraq coincided with the withdrawal of British troops from their last base in the southern city of Basra amid tensions between Washington and its main ally over their policy in Iraq.
Isenberg said: “Factions still run the city [Basra] – there is no rule of law.
“People feel compelled to join factions for their own safety. The region is still essentially a Wild West.”
The US president departed from Iraq shortly before 20:00 GMT on Monday, Cynthia Bergman, a White House spokeswoman, said.
Bush made the trip primarily to hold a “war council” with senior US and Iraqi officials before a report by General David Petraeus, the US commander in Iraq, on the effect of the “surge” in US troop levels.
“You are denying al-Qaeda a safe haven from which to plot and plan and carry out attacks against the United States of America,” he told US soldiers who roared their approval.
He landed in al-Anbar province, once a Sunni Arab fighter stronghold now seen by the US military as a success story.
The drop in violence in al-Anbar has been attributed to Sunni Arab leaders joining forces with the US military to combat al-Qaeda fighters.
But security officials said that shortly before Bush’s arrival, two car bombs went off in Ramadi, the provincial capital, killing four people and wounding 10.
In Baghdad, police found 15 corpses of men shot dead.
Marwan Bishara, Al Jazeera’s senior political analyst, said it would be political suicide for Bush to begin a real troop withdrawal in Iraq.
“The US cannot withdraw from the Iraq because it will be humiliating for the American empire.”