Capt. Bruce Kevin Clark was in Tarin Kowt, about 85 miles (140 kilometers) north of Kandahar, when he died during a Skype session with his wife.
Clarence Davis, a spokesman for the William Beaumont Army Medical Center in El Paso, Texas, where Clark was based, said that it has not been determined how Clark died and that the case is under investigation.
Clark's family said in a statement that they'd hoped for "a miracle" after his wife Susan saw what happened to Clark during their chat on Monday, but "it was not to be." They did not elaborate as to what took place.
"Although the circumstances were unimaginable, Bruce's wife and extended family will be forever thankful that he and his wife were together in his last moments," Clark's wife and family said Friday.
Clark -- known by many as Kevin -- was a chief nurse in the Army who amassed many honors in his military career, according to his family. Those include an Army Commendation Medal, Military Outstanding Volunteer Service, Global War on Terrorism Service Medal and an Army Service Medal.
The longtime resident of Spencerport, New York, joined the Army in September 2006 and served, among other places, at the Tripler Army Medical Center in Hawaii, according to a Beaumont Army Medical Center statement. More recently, he was based at that medical facility in southwest Texas and assigned to the Army's A Company, Troop Command.
"He loved being in the military," his sister-in-law Mariana Barry told CNN affiliate WHAM in upstate New York. "He was absolutely willing to make any sacrifice, and it's just horrible that this is the sacrifice he ended up making."
His commander described Clark, 43, as "awesome," "professional" and "a great asset, leader and friend," the family said.
After his death, special operations troops from the United States and Australia lined up to give him his final send-off from Afghanistan.
And on Thursday, his casket was wrapped in an American flag as it was transported off a military plane onto the tarmac of Dover Air Force Base in Delaware, according to the U.S. Air Force Mortuary Affairs Operation.
While no dates have been given, the family said that Clark's funeral will be in Spencerport and a memorial service will be held in Addison, Michigan.
In addition, New York Gov. Andrew Cuomo directed that all flags at state government buildings be flown at half-staff Monday in Clark's honor, as he's done with other Empire State troops who have died in combat zones.
In addition to his wife, Clark is survived by two daughters.
Dozens have posted comments on a Facebook tribute page set up in Clark's honor, some of them from people who knew him and his family personally and others from strangers wishing to thank him for his service.
"He was an excellent nurse, a fierce patient advocate, and loved to teach students. But what I remember most about him is the great love he had for his wife and beautiful little girls," one woman wrote. "I have no doubt that Bruce will be watching them and loving them forever more."
Barry said that her sister Susan is "being strong" for her daughters and that the entire family is committed to stepping up -- just like Clark did.
"We're going to try to take care of my sister and my nieces the way that Kevin would have taken care of them, and the way he would have wanted us to take care of them," Barry said.