After nearly nine years, 4,500 American dead, 32,000 wounded and more than $800bn (£517bn) spent, US officials have formally ended the war in Iraq with a highly symbolic ceremony during which an American forces flag was lowered.

Troops lowered the flag and wrapped it in camouflage, formally "casing" it, according to army tradition. The ceremony was attended by the US defence secretary, Leon Panetta, who told troops they leave Iraq with "lasting pride". Panetta said veterans of the nearly nine-year conflict could be "secure in knowing that your sacrifice has helped the Iraqi people to cast tyranny aside".

About 4,000 US soldiers remain in Iraq and many of those are due to leave in the next few days, departing a country still facing a weakened, but stubborn insurgency and political uncertainty.

The ceremony, at Baghdad international airport on Thursday, also featured remarks from General Martin Dempsey, the chairman of the joint chiefs of staff, and General Lloyd Austin, the top US commander in Iraq.

Austin has led the massive logistical effort of closing hundreds of bases and combat outposts, and methodically moving more than 50,000 US troops and their equipment out of Iraq over the past year.

During the ceremony, the US forces-Iraq flag was furled – or wrapped – around a flagpole and covered, to be taken back to the US.

On Wednesday, Barack Obama officially drew a line under the war. The president told troops in North Carolina that the US was peacefully leaving behind a stable nation and closing "one of the most extraordinary chapters in the history of the American military". He added: "There is something profound about the end of a war that has lasted so long."

During several stops in Afghanistan this week, Panetta made it clear that he thought the US could be proud of its accomplishments in Iraq, and that the cost of the bitterly divisive war was worth it.

"We spilled a lot of blood there," Panetta said. "But all of that has not been in vain. It's been to achieve a mission making that country sovereign and independent and able to govern and secure itself."

That, he said, was "a tribute to everybody: everybody who fought in that war, everybody who spilled blood in that war, everybody who was dedicated to making sure we could achieve that mission".

Panetta echoed Obama's promise that the US plans to keep a robust diplomatic presence in Iraq, foster a deep and lasting relationship with the nation and maintain a strong military force in the region.

US officials were unable to reach an agreement with the Iraqis on legal issues and troop immunity that would have allowed a small training and counter-terrorism force to remain. US defence officials said they expected there would be no movement on that issue until some time next year.

Despite Obama's earlier contention that all American troops would be home for Christmas, at least 4,000 forces will remain in Kuwait for some months. The troops will be able to help finalise the move out of Iraq, but could also be used as a quick reaction force if needed.

Obama met the Iraqi prime minister, Nouri al-Maliki, in Washington earlier this week, vowing to remain committed to Iraq as the two countries struggle to define their new relationship. Ending the war was an early goal of the Obama administration, and Thursday's ceremony allows the president to fulfil a crucial campaign promise at a politically opportune time. The 2012 presidential race is beginning, with Republicans fighting a ferocious battle to determine who will face Obama in the election.

Panetta acknowledged the difficulties for Iraq in the coming years, as the country tries to find its footing.

"They're going to face challenges in the future," Panetta said during a visit to troops in Afghanistan. "They'll face challenges from terrorism, they'll face challenges from those that would want to divide their country. They'll face challenges from just the test of democracy, a new democracy and trying to make it work. But the fact is, we have given them the opportunity to be able to succeed."

Over the coming days, US troops will leave Iraq in orderly caravans and tightly scheduled flights – a marked contrast to the shock and awe that rocked the country on 20 March 2003, as the US invasion began.