Kabul, Afghanistan (CNN) -- A man alleged to be a local Afghan policeman killed an American service member in eastern Afghanistan on Monday, while two British troops were shot and killed by an Afghan soldier in the southern province of Helmand, according to U.S., NATO and Afghan officials.
The British troops were killed outside a Provincial Reconstruction Team's headquarters in the southern city of Lashkar Gah, NATO and local officials said. Coalition forces then fatally shot the gunman.
A spokesman for the provincial governor said the incident stemmed from an argument the soldier had with the victims.
The eastern Afghanistan victim was an American soldier, a senior U.S. defense official, speaking on condition of anonymity, told CNN. NATO said he was shot as he approached an Afghan local police checkpoint; it said Afghan and coalition forces are investigating the incident but released no further details.
Monday's deaths bring to 93 the number of coalition service members who have died in Afghanistan this year, 44 of them Americans. In 2012 to date, 16 have been killed in what are euphemistically called "green on blue" attacks, meaning Afghan troops who have turned their weapons on allied forces.
In some attacks, insurgents have disguised themselves as Afghan soldiers in order to infiltrate bases. But the incidents have fueled mutual distrust at a critical juncture of the long-running conflict.
The latest killings come after a shooting rampage in Afghanistan this month left 17 villagers dead in the Panjwai district of southern Kandahar province. A U.S. soldier, Staff Sgt. Robert Bales, has been charged with murder in the slayings.
Speaking after the deaths of the two British soldiers on Monday, Gen. John Allen, the ISAF commander, said he could not discount revenge as a factor.
"I don't connect the two of those, but in any case it is prudent for us to recognize that, as you know, revenge is an important dimension in this culture," Allen told a briefing in Washington. "I have seen no indications yet that it has emerged as a potential factor, but we will certainly keep an eye on it."
Allen said ISAF officials are working on a new procedure to check the backgrounds of Afghans who sign up for the army or police force, and the Afghans "have taken a lot of steps themselves."
"They've worked very closely within the national director of security to place counterintelligence operatives inside their schools, inside their recruiting centers, and inside the ranks, the idea being to spot and assess the potential emergence of an individual who could be an extremist or, in fact, a Taliban infiltrator," he said.
But in an appearance at the Brookings Institution on Monday afternoon, he acknowledged that previous attacks by Afghan forces have led to "an erosion of trust."
"I believe that the relationship is very strong nonetheless," Allen added.
Disputes can arise from cultural misunderstanding, religious and ideological friction or combat stress, said Brig. Gen. Stephen Townsend, director of the Pakistan/Afghanistan Coordination Cell in the U.S. Joint Chiefs of Staff office.
Townsend said cultural training has been vital for U.S. soldiers, and now the Afghans are considering the same to provide a better understanding of Americans.
The Helmand governor on Monday praised ISAF troops for their sacrifices and assistance to the Afghan people.
"The enemies of the people and peace want to finish confidence among Afghan and ISAF forces, but they will never cover their evil aims by carrying out such violent acts," he said in a statement.
CNN's Mitra Mobasherat and Larry Shaughnessy and journalist Ruhullah Khapalwak contributed to this report.