President Bush today claimed progress in the war in Iraq, citing the killing Sunday of a top insurgent leader in Baghdad and growing capabilities of Iraqi troops. But he repeated a warning that upcoming votes in Iraq may be accompanied by a surge of violence.

Speaking in the White House Rose Garden after a briefing from two top military commanders, Bush said, "The support of Congress for our troops and our mission is important, and Americans need to know about the gains we've made in recent weeks and months. They need to know the way we're [adapting] our tactics and the way we're changing our strategy to meet the needs on the ground."

Bush urged Congress to listen carefully to the two Army generals -- Gen. John P. Abizaid, the commander of U.S. forces in the Middle East, and Gen. George W. Casey Jr., the top U.S. commander in Iraq -- who jointly briefed him this morning on the war.

He said they updated him on a raid in Baghdad in which U.S. and Iraqi forces "tracked down and killed Abu Azzam, the second most-wanted al Qaeda leader in Iraq." Bush was referring to Abdallah Najim Abdallah Muhammad Juwari, an Iraqi also known as Abu Azzam. He has been identified by the U.S. military as the "emir of Baghdad" for the insurgent group, al Qaeda in Iraq, which is headed by Jordanian terrorist Abu Musab Zarqawi.

"Abu Azzam was the operational commander for al Qaeda in Iraq and was responsible for the recent upsurge in violent attacks in the city since April 2005," the U.S. military said in a statement yesterday. It said that as the group's chief in Baghdad, Abu Azzam "reportedly directed and controlled all terrorist activity and operations in and around the city."

Al Qaeda in Iraq denied yesterday that Abu Azzam was Zarqawi's deputy, calling him merely a "soldier" for the group and the leader of an active brigade in Baghdad. If he was, in fact, killed, the group said in a statement posted on the Internet, "we congratulate him for being a martyr."

Appearing in the Rose Garden flanked by Vice President Cheney, walking with a cane after his recent leg surgery, and the two generals, Bush said of Abu Azzam, "This guy was a brutal killer. He was one of Zarqawi's top lieutenants. . . . He was one of the terrorists responsible for the recent upsurge in attacks in the Iraqi capital, which is part of their campaign to stop a referendum on the Iraqi constitution and is part of their efforts to break the will of the American people and the will of our coalition."

Iraq is scheduled to hold a referendum Oct. 15 to ratify a new constitution. If it passes, elections for a new government to be formed under that constitution would be held in December.

Bush said that in addition to "hunting down high-valued targets like Azzam and Zarqawi," U.S. forces are "coordinating aggressive counterterrorism operations" and training more Iraqi forces.

"The growing size and increasing capability of the Iraqi security forces are helping our coalition address the challenge we have faced since the beginning of the war," Bush said. "By leaving Iraqi units in the cities we've cleared out, we can keep the cities safe while we move on to hunt down the terrorists in other parts of the country."

He cited recent successes in northwestern Iraq near the Syrian border, notably in the town of Tall Afar, where he said "Iraqi security forces outnumbered coalition forces for the first time in a major offensive operation."

Bush made no mention of an attack today in which a female suicide bomber blew herself up outside a military office in Tall Afar, killing herself and at least five other people and wounding dozens of others. The target was described variously as a U.S. military center where people filed compensation claims and as an Iraqi army recruiting office.

According to the SITE Institute, a Washington-based organization that monitors radical Islamic Internet sites, al Qaeda in Iraq claimed responsibility for the Tall Afar bombing, saying it was carried out by a female member of the group and aimed at "converted volunteers" in Tall Afar.

Bush said in his Rose Garden speech, "Because of our joint efforts, hundreds of terrorists have been killed or captured or flushed, which makes it more difficult for the foreign terrorists to enter Iraq through the northwest route" from Syria. He said more than 100 Iraqi battalions are now operating, more than 20 of them in Baghdad.

But he warned, "The terrorists have a history of escalating their attacks before Iraq's major political milestones." He said "increasing violence" can be expected ahead of next month's referendum and the elections in December.

"They can't stand elections," Bush said. "The thought of people voting is an anathema to them."

The insurgents will "do everything in their power to try to stop the march of freedom," Bush said. "And our troops are ready for it." He predicted that "the terrorists will fail."

Bush left immediately after the speech without answering any questions from reporters.