BAGHDAD — The U.S. military began flying 2,000 Georgian troops home from Iraq on Sunday, military officials said, after the Georgians recalled the soldiers following the outbreak of fighting with Russia in the breakaway province of South Ossetia.

The decision was a timely payback for the former Soviet republic that has been a staunch U.S. supporter and agreed to send troops to Iraq as part of the U.S.-led coalition.

Georgia was the third-largest contributor of coalition forces after the U.S. and Britain, and most of its troops were stationed near the Iranian border in southeastern Iraq.

The U.S. military has played down concerns about the redeployment, saying it may have "some impact" in the near term but no significant long-term effect on Iraq's security.

"We want to thank them for the great support they've given the coalition and we wish them well," military spokesman Rear Adm. Patrick Driscoll said earlier Sunday at a news conference.

Georgia, which borders the Black Sea between Turkey and Russia, had asked the U.S. military on Friday to provide transportation.

"We are supporting the Georgian military units that are in Iraq in their redeployment to Georgia so that they can support requirements there during the current security situation," said Col. Jerry O'Hara, another military spokesman in Baghdad. "Flights have in fact begun today and Georgian forces are redeploying."

He declined to disclose flight details. But another senior U.S. official, who spoke on condition of anonymity because he wasn't authorized to release the information, said the military would fly the troops back "to the republic of Georgia.

The officials also said American units had been shuffled in their area of responsibility to compensate for the departure of the Georgians.

O'Hara said that even though the loss of forces was unexpected, "we can and are accommodating the changes."

Most Georgian troops moved last year from the relatively safe Green Zone in Baghdad to an area southeast of the capital to help interdict supplies allegedly being smuggled to Shiite extremists from Iran. More than 100 remained in Baghdad to help secure the Green Zone.

At least five Georgians soldiers have died in Iraq since the U.S.-led invasion in 2003.

Some Iraqis welcomed the Georgian withdrawal, saying they're tired of the presence of U.S-led foreign troops.

"God willing, not only the Georgian forces will withdraw but all other troops will leave our country and security and stability will come back to our land," Baghdad resident Ghada Adnan told Associated Press Television News.

Georgia, whose troops have been trained by American soldiers, began an offensive to regain control over South Ossetia overnight Friday, launching heavy rocket and artillery fire and air strikes.

In response, Russia, which has granted passports to most South Ossetians, began overwhelming bombing and shelling attacks against Georgia and Georgian troops.