Bush, whose personal approval ratings have been dragged down by a combination of Iraq and the fallout from the Hurricane Katrina debacle, warned on Wednesday, however, that violence could surge before Iraqis vote on a new constitution next month.
He said US troops were ready and would not let "terrorists" obstruct the "march of freedom", apparently trying to convince Americans of progress in Iraq, despite the deaths of more than 1900 US troops since March 2003.
"Our strategy is clear in Iraq. We are hunting down high-value targets," Bush said, highlighting the killing of Abu Azzam, who the US military and Iraqi government said was al-Qaida's No 2 in the country.
"This guy is a brutal killer," Bush said.
Al-Qaida has denied that Abu Azzam, also known as Abd Allah Nahim but whose real name was Abd Allah Mohammed al-Juhaari, was its second in command in Iraq.
Despite his demise, Bush warned of the likelihood of more violence in the run-up to a referendum on a draft post-Saddam Hussein constitution next month and elections due before mid-December.
Bush expects more violence
before the charter referendum
"As these milestones approach, we can expect there to be increasing violence from the terrorists," Bush said, after a briefing from US Central Command chief, General John Abizaid, General George Casey, commander of US forces in Iraq and Chairman of the Joint Chiefs of Staff Richard Myers.
Despite his outlining of progress in halting fighters' infiltration of Iraq and in the training of Iraqi troops, Bush's statement did not contain new material or initiatives to stem violence in the country.
But Bush, in an apparent sign of concern about restiveness in Congress over the human, diplomatic and financial cost of the US presence in Iraq, unusually called directly on key members of both parties to heed the generals' message.
"As these milestones approach, we can expect there to be increasing violence from the terrorists"
US President George Bush
"I urge the members of Congress to attend the briefings with generals Abizaid and Casey," he said in the televised statement from the White House Rose Garden.
"I urge them to ask questions about our efforts in Iraq and to listen carefully about the type of war we fight.
"The support of Congress for our troops and our mission is important, and Americans need to know about the gains we have made in recent weeks and months."
Congressional opponents of the continuing US presence in Iraq are circulating a joint resolution which would require Bush to announce a timetable for withdrawal by the end of the year, and begin drawdowns in 2006.
The White House and its top ally, British Prime Minister Tony Blair, have argued that such a step would send a signal of softening resolve that would embolden fighters in Iraq.
Bush's ratings have suffered from
the Hurricane Katrina debacle
They also argue it would be wrong to abandon the Iraqi people, as they trek along the painful path to democracy.
According to a CNN/USA Today Gallup poll released a week ago, support for Bush's management of the war in Iraq dropped to 32%.
A Wall Street Journal/NBC News poll released on 15 September showed his overall ratings had sunk to 40%, a record low.
About 55% of those polled supported bringing US troops home from Iraq, while 36% supported Bush's policy of keeping the troops in place until peace can be guaranteed.
Britain's Foreign Secretary Jack Straw on Wednesday also warned of more dark moments ahead in Iraq.
He spoke of the difficulties of nation-building, after British troops were stoned and petrol-bombed by rioters earlier this month.
"None of us should underestimate the challenges that still lie ahead in Iraq. Nation-building from a violent past has never been easy"
Britain's foreign secretary
Addressing the governing Labour Party's annual conference, Straw cautioned that it would take time to rebuild a country that suffered a dictatorial, violent past.
"None of us should underestimate the challenges that still lie ahead in Iraq," Straw said. "Nation-building from a violent past has never been easy."
Straw was heckled by an elderly delegate who shouted "That's a lie" as the foreign secretary justified the continued presence of British troops in Iraq.
The man was removed from the conference hall by stewards, prompting complaints from other delegates.
Cannot force democracy
But unlike previous years, where anger over the US-led invasion dominated the sidelines of the conference, criticism of the war was muted and largely absent.
During a debate on Britain's foreign policy, Iraq was mentioned by only one speaker, trade unionist Barry Camfield.
"Our troops should be pulled out now and quickly. You cannot force democracy on a people by means of war"
Trade unionist Barry Camfield
"Our troops should be pulled out now and quickly," he told the conference hall, drawing some cheers and applause.
"You cannot force democracy on a people by means of war."
Prime Minister Tony Blair has resisted calls to withdraw Britain's 8500 troops from Iraq, saying he is committed to help the fledgling government there restore order and build democratic institutions.