The United States military officially declared an end to its mission in Iraq on Thursday even as violence continues to plague the country and the Muslim world remains distrustful of American power.

In a fortified concrete courtyard at the airport in Baghdad, Defense Secretary Leon E. Panetta thanked the more than one million American service members who have served in Iraq for “the remarkable progress” made over the past nine years but acknowledged the severe challenges that face the struggling democracy.

“Let me be clear: Iraq will be tested in the days ahead — by terrorism, and by those who would seek to divide, by economic and social issues, by the demands of democracy itself,” Mr. Panetta said. “Challenges remain, but the U.S. will be there to stand by the Iraqi people as they navigate those challenges to build a stronger and more prosperous nation.”

The tenor of the farewell ceremony, officially called “Casing the Colors,” was likely to sound an uncertain trumpet for a war that was launched to rid Iraq of weapons of mass destruction it did not have and now ends without the sizable, enduring American military presence for which many officers had hoped. The tone of the string of ceremonies culminating with the final withdrawal event on Thursday has been understated in keeping with an administration that campaigned to end an unpopular war it inherited. Although the ceremony on Thursday marked the end of the war, the military still has two bases in Iraq and roughly 4,000 troops, including several hundred that attended the ceremony. At the height of the war in 2007 there were 505 bases and over 150,000 troops.

According to military officials, the remaining troops are still being attacked on a daily basis, mainly by indirect fire attacks on the bases and road side bomb explosions against convoys heading south through Iraq to bases in Kuwait

Even after the last two bases are closed and the final American combat troops withdraw from Iraq by Dec. 31 under rules of an agreement with the Baghdad government, a few hundred military personnel and Pentagon civilians will remain, working within the American Embassy as part of an Office of Security Cooperation to assist in arms sales and training.

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