(CNN) -- America's top military official Thursday sent his regrets to Pakistan's army chief of staff over the U.S. helicopter strike that killed two Pakistani soldiers, his office said.
Adm. Mike Mullen, chairman of the Joint Chiefs of Staff, told Gen. Ashfaq Parvez Kayani that the September 30 incident near the Afghan border was most "regrettable" and he passed along his "sincere condolences" for the deaths.
"The death of our soldiers in combat is always tragic, but under these circumstances, it is even more difficult to accept," he said in a letter this week.
Mullen consults regularly with Kayani and has visited Pakistan 20 times since becoming chairman three years ago.
"Please know that the families of the soldiers lost in this tragic incident are in our constant thoughts and prayers. I think you already know, but I want to reinforce, that we take this incident very seriously and our most senior commanders in theater will review the investigation thoroughly with an eye toward avoiding recurrence of a tragedy like this. As always, thanks for your leadership of your Army, but especially in difficult times and circumstances such as this."
NATO's International Security Assistance Force said two Pakistani border guards were killed in the incident, and a coalition-Afghan assessment determined that there needs to be better coordination between the United States and Pakistan.
The incident spurred a major headache for the coalition -- Pakistan's closure of the main land route for NATO supplies heading from Pakistan to Afghanistan: the Torkham border crossing.
The incident began when ISAF troops saw what it believed was a group of insurgents attempting to fire mortars at a coalition base in the border area of Dand Patan district in Afghanistan's Paktiya Province.
An ISAF air weapons team was called to provide fire support and engaged the suspected insurgents' firing position, located inside Afghanistan along the border area, the release said.
ISAF aircraft did enter into Pakistani airspace briefly as they engaged this initial target.
After the initial strike, the aircraft received what the crews assessed as effective small arms fire from individuals just across the border in Pakistan. Operating in self defense, the ISAF aircraft entered into Pakistani airspace killing several armed individuals.
The initial assessment of the incident issued on Wednesday shows that coalition forces mistook ground fire for insurgent activity.
"We believe the Pakistani border guard was simply firing warning shots after hearing the nearby engagement and hearing the helicopters flying nearby," said U.S. Air Force Brig. Gen. Tim Zadalis, the ISAF assessment team leader.
"This tragic event could have been avoided with better coalition force coordination with the Pakistan military."
Anne W. Patterson, the U.S. ambassador to Pakistan, also apologized to Pakistan on behalf on the American people "for the terrible accident," and Gen. David Petraeus, ISAF commander, offered his condolences.
"We deeply regret this tragic loss of life and will continue to work with the Pakistan military and government to ensure this doesn't happen again," he said.