"Staff Sgt. Joe Lemm served this nation with the selflessness and bravery that embodies the U.S. Armed forces and the NYPD," Cuomo said in a statement.

"On behalf of all New Yorkers, I extend my deepest condolences to his family, friends, fellow officers and service members."

Lemm, 45, was a 15-year NYPD veteran who was promoted to detective in January 2014, serving in the Bronx warrant squad, according to a statement from Police Commissioner Bill Bratton.

As a member of the NYPD, Lemm was deployed three times, twice to Afghanistan and once to Iraq.

Joseph Lemm.

Lemm -- a resident of West Harrison, New York, assigned to the 105th Security Forces Squadron, which is a part of the 105th Airlift Wing at Stewart Air National Guard Base in Newburgh -- leaves behind his wife and two children.

Others identified

The Air Force on Tuesday identified the six people who died in a news release, listing their ages, hometowns and units.

Among them was Maj. Adrianna Vorderbruggen of the Air Force. A pioneer in the protest against the military's former "don't ask, don't tell" policy, she was one of the first openly gay service members to marry after the policy was ended in 2011. The group Military Partners and Families Coalition confirmed her death on its Facebook page.

"Major Vorderbruggen leaves behind her wife, Heather, and son, Jacob," the group said. "We do find comfort in knowing that Heather and Jacob are no longer in the shadows and will be extended the rights and protections due any American military family as they move through this incredibly difficult period in their lives."

She was 36.

Another service member killed Monday was from Stewart Air National Guard Base, according to Orange County Executive Steven Neuhaus. He was not identified, but CNN spoke to Diana Bonacasa, who said her son, Louis Bonacasa, had died. Louis Bonacasa, 31, was on his fourth tour of duty in the region.

He was married and had a 5-year-old child.

"I've never seen a man love a family the way he loved his," Diana Bonacasa said.

She said her son, who lived in Manorville, New York, was proud of serving his country and was a "man of integrity."

He had joined the military 14 years ago after the United States had invaded Afghanistan. He told his mother he wanted to join the special operations forces in the Air Force but couldn't because of sight issues.

Chester McBride, a 2003 graduate of Statesboro High School in Georgia, was also identified Tuesday as one of the service members killed in the blast, CNN affiliate WSAV reports. McBride, 30, was a graduate of Savannah State University, his family told the station.

The Air Force identified the others killed as Staff Sgt. Michael A. Cinco, 28, of Mercedes, Texas, and Staff Sgt. Peter W. Taub, 30, of Philadelphia.

Bomber on motorcycle

A suicide bomber on a motorbike carried out the attack on a joint patrol of Afghan and coalition forces at about 1:30 p.m. in the Bajawri area of Bagram district, said Waheed Sediqi, a spokesman for the governor of Parwan province.

Two other U.S. service members and an American contractor were also wounded, officials said.

The area is close to the U.S. base in the Bagram district of northern Parwan province.

The last time six U.S. service members were killed was October 2, when their C-130J Super Hercules aircraft crashed shortly after takeoff from Jalalabad Airfield, Afghanistan.

On July 8, 2012, six U.S. soldiers were killed after an improvised explosive device attack in Maidan Shahr, Wardak province, Afghanistan.

This week, Carter expressed his condolences to the Americans' families.

"As I saw firsthand during my visit to Afghanistan last Friday, our troops are working diligently alongside our Afghan partners to build a brighter future for the Afghan people," Carter said in a statement. "Their dedicated efforts will continue despite this tragic event."

White House press secretary Josh Earnest in a statement condemned the "cowardly attack," and said the United States "will continue to work together to promote peace and stability in Afghanistan."

Claim of responsibility

The Taliban took credit for the attack.

The attack remains under investigation, said U.S. Col. Michael Lawhorn, a spokesman for NATO's Operation Resolute Support.

The six people killed Monday bring the tally of NATO service members who have died in Afghanistan this year to 25. The death toll has steadily declined year by year since reaching a peak of 711 in 2010.

The number of U.S. troops in Afghanistan stands at just under 10,000, down from its peak of 100,000 in 2010.

Taliban takes control of key district in Helmand Province

According to NATO, the operation was launched in January "to provide further training, advice and assistance for the Afghan security forces and institutions." The mission involves 12,000 personnel from NATO and 14 partner nations.

Its central hub is in Bagram/Kabul with "spokes" in Mazar-e Sharif, Herat, Kandahar and Laghman, NATO says.