The Afghan president, Ashraf Ghani, expressed his "profound sorrow" over the tragedy and ordered an investigation into the killings.
The incident happened as coalition helicopters were flying over an area in Logar province where clashes were underway between Afghan troops and Taliban fighters, the Afghan Ministry of Defense said.
Insurgents fired toward the helicopters, prompting a response that destroyed one army checkpoint, the ministry statement added. An unspecified number of the army members were "killed and wounded," the ministry said, adding that the incident was under investigation.
Logar provincial army commander Abdul Razaq said the early morning strike took place in the district of Baraki Barak, about 50 kilometers (30 miles) east of Kabul. Razaq revised an earlier higher figure and said that seven troops were killed while five were wounded in the strike.
Logar police chief Mohammad Douod Ahmadi confirmed those casualty figures. Conflicting number of casualty figures are common during fighting in remote areas inaccessible to reporters.
District governor Mohammad Rahim Amin said the NATO airstrike was "likely a mistake, due to bad coordination" in an area where Taliban insurgents are highly active.
A U.S. military spokesman in Afghanistan, Col. Brian Tribus, said the coalition is aware of an incident in Logar and is investigating it.
According to a statement from Ghani's office, the Afghan president appointed a team to "comprehensively probe the incident and come up with clarification surrounding the airstrike." Ghani also urged the international forces to "take maximum precautions" not to harm Afghan civilians and troops in their future operations.
Security in Logar has deteriorated in recent months as the Taliban stepped up their attacks on Afghan soldiers and security forces, trying to spread their footprint across the country and take control of some remote regions.
The U.S. and NATO forces concluded their combat mission at the end of last year and Afghan troops have since taken control of the country's security, which has caused their casualties to spike.