The suicide bombing also injured four American troops, who are said to be in stable condition with wounds that are not life-threatening.
The statement identified the soldiers who died as Spc. Christopher Harris, 25, of Jackson Springs, N.C., and Sgt. Jonathon Hunter, 23, of Columbus, Ind. Both were infantrymen assigned to 2nd Battalion, 504th Parachute Infantry Regiment, 1st Brigade Combat Team, 82nd Airborne Division.
"Chris and Jon lived and died as warriors," Col. Toby Magsig, commander of 1st Brigade Combat Team, said in the statement. "They will always be a part of the legacy of the Devil Brigade and their memory lives on in the hearts and minds of their fellow paratroopers. Our thoughts and prayers are centered on the families and loved ones of these two great Americans."
Jonathon Hunter's father, Mark Hunter, said the Indiana National Guard informed him Wednesday night that his son died in the attack on a NATO convoy near the southern Afghan city. He said the Indiana soldier was just 32 days into his first deployment.
Britt Harris, the wife of Spc. Christopher Harris, announced her husband's death on her Facebook page.
"As the news spreads about the two soldiers killed in action yesterday in Afghanistan it is with a very heavy and broken heart that I confirm one of them was my husband Chris Harris," she wrote. "We had recently discovered I am in the very early weeks of pregnancy. Right now that is my main concern and I want to try and make sure everything continues to be healthy considering these crushing circumstances."
Britt Harris told a CBS news station in North Carolina that she and her husband had recently moved to Carthage, N.C., before he deployed.
Jonathon Hunter, who grew up about 40 miles south of Indianapolis, left July 1 on his first deployment and was providing security for the convoy that was attacked, his father said. He joined the Army in 2014 and was a member of the 1st Brigade Combat Team, 82nd Airborne Division at Fort Bragg.
Mark Hunter said his son was excited about his first deployment, but that he, as an Army veteran, was apprehensive.
"He had been there 32 days. I'm former military, me and his uncle both, so we know the dangers," Hunter told The Associated Press by phone from his home in Columbus.
He said his son, who got married last October and has an older brother and two stepsisters, was cheerful, loving and religious.
"If you were down, he would cheer you up and he was God-loving. He was raised in the church," he said.
Mark Hunter said he will travel Friday to Dover Air Force Base, Del., to retrieve his son's body, and that funeral plans were being determined.
After graduating from Columbus East High School in 2011, Jonathon Harris spent a short time in Nashville pursuing his dream of becoming a music producer, his father said. He later enrolled at Indiana State University, where he studied criminology and business.
Mark Hunter said his son eventually left ISU and joined the Army in April 2014 to help pay for his education.
"After he got into school -- and of course we were struggling with bills, to pay for it -- he decided to join. He said, 'Dad, I know that going into the military I can get a free education,'" said Mark Hunter, who added his family has a history of military service that dates back to the Civil War.
"I'm just proud of him," Mark Hunter said. "He was a great soldier. He made [sergeant] in a little over three years, which is pretty rare, they tell me."
Before Jonathon Hunter's death, 207 Indiana servicemembers had died since 2002 in the war in Afghanistan or Iraq, or supporting those operations, said Tim Dyke, director of training and services Indiana Department of Veterans Affairs. He said that's based on a tally produced by the agency's former director.
--Rick Callahan at the Associated Press contributed to this report.