Suspected al-Qaida fighters killed two Iraqi soldiers early Thursday, then stole their Humvees to ambush rival Sunnis south of Baghdad, the Mulit-National Force-Iraq tells FOXNews.

A series of mortars later struck the U.S.-protected Green Zone, Iraqi police said. The attack coincided with the celebration of Thanksgiving but there were no immediate reports of casualties in the heavily fortified area, which houses the U.S. Embassy, thousands of American troops and contractors, and Iraqi government headquarters.

About 10 blasts were heard in central Baghdad just before 5 p.m., and a huge plume of black smoke rose into the sky as the sun was setting. The U.S. government public address system in the Green Zone also warned people to "duck and cover" and to stay away from windows.

The attack by the al-Qaida fighters south of Baghdad began when they targeted an Iraqi army patrol near the rural area of Hawr Rijab, killing three soldiers and commandeering two Humvees, according to a local police report.

The militants then drove in the Humvees to the nearby headquarters of a group of Sunnis who have turned against the terror network and formed a so-called Awakening Council.

Fierce clashes broke out, killing seven people, the MNFI tells FOXNews.

Associated Press Television News footage showed Iraqi police and soldiers forming a protective cordon around wailing women and children as they loaded wooden coffins onto the cars for funeral processions of those killed.

Northeast of the capital, Iraqi security forces killed 19 al-Qaida fighters in Baqouba, police said, adding that two civilians also died and two others were wounded in the crossfire.

The U.S. military has claimed a large measure of success in quelling the violence in Baqouba, which was an al-Qaida stronghold some 35 miles northeast of Baghdad. But pockets of resistance remain there and elsewhere, underlining fears about the fragility of security gains made in recent months with the influx of troops and the swelling of popular movements against extremists.

In another example, a suicide car bomber blasted a police checkpoint outside a courthouse on Wednesday, killing up to six people and wounding as many as 22 in Ramadi, the capital of Anbar province and the site of the genesis of the anti-al-Qaida sentiment among Sunni tribal leaders and even some former insurgents.

Iraqi security forces also found 40 decomposed bodies on Wednesday, including women and children, north of Ramadi near Lake Tharthar in an area controlled until recently by al-Qaida in Iraq.

The victims had been shot and did not have ID cards with them, although it could not be determined when they were killed, an Iraqi army officer said, also declining to be identified because the information was confidential.

The mass grave unearthed near Ramadi was the latest in a series of such finds as Iraqis from both Islamic sects step up patrols of areas after ousting extremists.

Nationwide, the U.S. military maintains attacks have fallen 55 percent since a troop buildup over the summer because stepped up American military operations have driven Sunni and Shiite extremists from most of their longtime strongholds around the city.

But U.S. commanders have been careful to avoid declaring victory over al-Qaida in Iraq and other extremist organizations, acknowledging militants have fled the security crackdowns to other parts of the country.

Several Iraqi refugees returned home to Baghdad from Syria on Thursday, saying they felt confident about the dramatic drop in the level of sectarian attacks.

"Thanks to be for God that we arrived here today. We have learned that the security situation improved and we hope all Iraqis will get back to Iraq," Muhanad Ibrahim said as he arrived in the western neighborhood of Mansour.

Thousands of Iraqis living in Syria have headed back home in the past weeks.

A bus bound from Syria with heaps of luggage tied to the roof was one of two that were greeted by relatives who cheered and hugged the returned refugees as they got off.

While many are relieved about the improved security situation, the move also has been attributed to harsh visa requirements imposed by Syria since last month that make it more difficult for Iraqis to stay in the neighboring country.

The Iraqi government also has started to organize free trips for those who want to return home, offering protected convoys and even flights.

The New York Times, meanwhile, quoted senior American military officials as saying that Saudi Arabia and Libya were the source of about 60 percent of the foreign fighters who came to Iraq in the past year to serve as suicide bombers or to facilitate other attacks.

The report said that data came largely from documents and computers discovered in September, when a U.S. raid near the Syrian border targeted insurgents believed to be responsible for smuggling the vast majority of foreign fighters into Iraq.

A key discovery was a listing of hometowns and other details for more than 700 fighters brought into Iraq since August 2006, the newspaper said, according to the U.S. officials who were not further identified. Saudis accounted for the largest number of fighters listed with 305, followed by Libyans with 137. United States officials have previously offered only rough estimates of nationalities of such fighters.

The Associated Press contributed to this report.