(CNN) -- Stung by online comments calling it "disgusting" and "un-American," Delta Air Lines on Wednesday announced it will allow U.S. military personnel traveling on orders to check more bags for free.

The policy change, which is effective immediately, came a day after U.S. Army soldiers returning from Afghanistan complained that they were charged almost $3,000 in bag fees by the carrier.

"We regret that this experience caused these soldiers to feel anything but welcome on their return home," wrote Rachael Rensink, manager of Delta Social Media, in an updated post on the carrier's blog.

The Delta incident sparked outrage online after the servicemen spoke out about their experience in a video posted on YouTube.

In the clip -- which the men say was recorded on board a Delta flight from Baltimore to Atlanta on Tuesday, a day after they returned from Afghanistan -- the soldiers explain they had "a little issue with the bags."

CNN affiliate WXIA in Atlanta identified the soldiers as U.S. Army Staff Sgts. Fred Hilliker and Robert O'Hair.

The men, who were bound for Fort Polk, Louisiana, said their military travel orders allowed them to carry up to four bags, but when they arrived at the airport in Baltimore, Delta told them it allows military personnel to check only three bags for free.

Members of the unit who were traveling with four bags ended up paying out of pocket for their extra luggage, the soldiers said in the video. They were charged $200 per extra bag, so the 34-member unit ended up paying more than $2,800 in bag fees, the soldiers added.

Any extra bag fees charged by an airline will be reimbursed by the government, a military spokeswoman told CNN affiliate WGCL in Atlanta.

One of the soldiers in the video said the bag he had to pay for was a weapons case that contained "the tools that I used to protect myself and Afghan citizens while I was deployed in the country."

The other man then looked into the camera, exasperated.

"Good business model, Delta," he said sarcastically. "Not happy, not happy at all," he added, shaking his head.

The airline apologized for "any miscommunication" about its bag allowances, but reiterated that its policy for U.S. military personnel allowed them to check up to four bags in First/Business class and three bags in coach for free.

Other airlines, such as United, American, Continental and US Airways, have had or continue to have similar rules.

On Wednesday, Delta changed its policy and said U.S. military personnel traveling on orders would now be allowed to check up to four bags for free in coach and up to five bags at no charge in First and Business Class.

In wake of the Delta incident, United/Continental announced Wednesday it was also allowing more bags.

"United and Continental are waiving the fourth checked bag fee for military personnel traveling on orders in recognition of their sacrifice and service to our country," Christen David, a spokeswoman for United/Continental Airlines, said in an e-mail.

The two airlines closed a merger deal in October.

Delta said it deeply respects and admires men and women in uniform and added that it has worked hard to ensure that U.S. military personnel get "additional flexibility" when they travel on the carrier.

The carrier said it's "continuing to work with the soldiers individually to make this situation right for each of them."

The soldiers may have been misinformed about how many bags traveling active duty military personnel can check for free, Stars and Stripes reported.