The operation was targeting ISIS-K, the terror group's Afghanistan affiliate. A US official told CNN the wounded soldier's injuries are not considered life-threatening.
The Pentagon identified the two slain soldiers Friday as Sgt. Joshua P. Rodgers, 22, of Bloomington, Illinois, and Sgt. Cameron H. Thomas, 23, of Kettering, Ohio. They were assigned to 3rd Battalion, 75th Ranger Regiment, based in Fort Benning, Georgia.
"The fight against ISIS-K is important for the world, but sadly, it is not without sacrifice," said Gen. John W. Nicholson, commander of US Forces-Afghanistan. "On behalf of all US forces and our coalition partners, I offer our deepest sympathies to the families, friends and fellow service members of our fallen comrades."
Achin District is the primary base of operations for ISIS in Afghanistan and has been the site of multiple joint US-Afghan counterterrorism missions. A US Army Special Forces soldier was killed fighting the terror group there earlier this month.
It is also where the US dropped one of its most powerful bombs earlier this month, killing close to 100 ISIS fighters, according to Afghan officials.
Nicholson has pledged to eliminate ISIS-K from Afghanistan this year.
"We're going to keep going until they're defeated in 2017," Nicholson told reporters in Kabul this month.
Beginning in 2016, Afghan security forces backed by US military advisers have launched a major offensive against ISIS, with Nicholson saying that the terror group has lost about half of its fighters and been ejected from two-thirds of its territory.
The latest counter-ISIS push began in March of this year.
US officials estimate that ISIS has about 600 to 800 fighters in the country, largely formed from former members of other regional terror groups, including the Pakistani Taliban and Islamic Movement of Uzbekistan. ISIS is believed to be behind a series of terror attacks, including the recent deadly attack on a hospital in Kabul.
There are about 8,400 US troops in Afghanistan. The US counterterrorism mission is separate from the NATO-led effort to train, advise and assist the Afghan army and police force in its fight against the Taliban.
US and coalition casualties in Afghanistan are rare, having fallen dramatically since the Afghan government assumed responsibility for combat operations in 2014.