U.S. Defense Secretary Leon Panetta has formally declared the end of the war in Iraq, at a ceremony at the airport in Baghdad.

After the U.S. command's flag was lowered and the “Last Post” was played Thursday, Panetta told troops that a lot of American and Iraqi blood was spilled, but that the mission of an Iraq that could govern itself has become real.

More than 4,500 U.S. troops died as well as tens of thousands of Iraqis during the allied operation in Iraq that toppled Saddam Hussein. More than 32,000 U.S. soldiers were wounded. The war cost the United States at least $800 billion.

Panetta acknowledged that Iraq is still facing many challenges.

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

There were about 4,000 U.S. troops remaining in Iraq Thursday, down from as many as 170,000 at the height of the war. The remaining U.S. soldiers are set to withdraw from Iraq by December 31.

Panetta said those soldiers will leave Iraq knowing they helped the Iraqi people begin a new chapter in their history that is “free from tyranny” and full of hope for prosperity and peace.

He said Iraq is now responsible for directing its own future, but that the U.S. will remain a partner with a “significant” diplomatic presence in Iraq.

“This is a time for Iraq to look forward. This is an opportunity for Iraq to forge ahead on the path to security and prosperity, and we undertake this transition today reminding Iraq that it has in the United States a committed friend and a committed partner. We owe it to all of the lives that have been sacrificed in this war not to fail.”))

Panetta arrived in Baghdad after a visit to Djibouti and Afghanistan. He left Iraq for neighboring Turkey to discuss defense cooperation with the U.S. ally.

The United States formally ended combat operations in Iraq in August of last year, and U.S. troops have been advising and assisting Iraqi forces as they assumed full responsibility for protecting their country.

Former U.S. president George W. Bush ordered the invasion of Iraq in 2003, citing reports that the country had weapons of mass destruction. No such weapons were ever found.

U.S. President Barack Obama pledged to end the war when he took office. On Wednesday, he paid tribute to those who served in the war, and said the United States is leaving behind a sovereign, stable and self-reliant Iraq. He described that as an “extraordinary achievement,” as he spoke at the Fort Bragg military base in North Carolina.

Mr. Obama said the future of Iraq is now in the hands of the Iraqi people.