Standing outside the Oval Office of the White House, Mr. Bush also announced that effective Thursday, the duration of troop tours in Iraq will be cut from 15 months to 12 months.
Mr. Bush said this reduction "will relieve the burden on our forces and it will make life easier for our wonderful military families."
The president's updated report on Iraq was delivered on short notice to the White House press corps. It came with the war in its sixth year and violence on the ground substantially decreased in recent weeks.
He said that commanding Gen. David Petraeus and U.S. Ambassador Ryan Crocker, however, "caution that the progress is still reversible, and they report that there now appears to be a degree of durability to the gains that we have made."
"We are now in our third consecutive month with reduced violence levels holding steady," Mr. Bush said.
Looking ahead to the next recommendation on troop levels from U.S. military leaders, Mr. Bush said he expects "further reductions in our combat forces, as conditions permit."
"The progress in Iraq has allowed us to continue our policy of return on success," he said. "We have now brought home all five of the combat brigades and the three Marine units that were sent to Iraq as part of the surge. The last of these surge brigades returned home this month."
Some 147,000 troops remain on the ground in Iraq.
Mr. Bush said the United States and Iraq also are pressing forward with talks on an agreement that would set the terms for any future U.S. presence and noted that Prime Minister Nouri al-Maliki recently had a productive visit with other foreign leaders.
"We are also making progress in the discussion with Prime Minister Maliki's government on a strategic framework agreement. This agreement will serve as the foundation for America's presence in Iraq once the U.N. resolution authorizing the multinational forces expires on Dec. 31," the president said. "We remain a nation at war. Al Qaeda is on the run in Iraq, but the terrorists remain dangerous and they are determined to strike our country and our allies again."
The White House had hoped that it would have completed by Thursday the long-term agreement with al-Maliki's government. But negotiations with Baghdad have been difficult and have spawned many disputes, including the question of setting timelines for troop withdrawals. The best hope now seems to be only a stopgap agreement by the end of the year.