The Department of Defense confirmed the deaths of Sgt. Jonathon Michael Hunter, 23, of Indiana, and Spc. Christopher Michael Harris, 25, of North Carolina.
Both soldiers were assigned to 2nd Battalion, 504th Infantry Regiment, 1st Brigade Combat Team, 82nd Airborne Division, Fort Bragg, N.C.
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.
The family is planning a public memorial service in his honor.
The U.S. military in Afghanistan earlier said that four other American troops were wounded in Wednesday's attack.
A U.S. official on Wednesday said the convoy was on a routine training, advisement and assistance mission when it was attacked. The Taliban has claimed responsibility.
A statement from Resolute Support, the NATO-led mission in Afghanistan, said the attack was on a NATO convoy.
The deaths raise the number of U.S. service members killed in action in Afghanistan so far this year to nine, matching the total for all of 2016.
The Associated Press contributed to this report
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