Correction: An earlier version of this article inaccurately reported the number of NATO troops who have been killed by Afghan security forces since May 2007. This version has been corrected.

An Afghan soldier killed two British troops in southern Afghanistan and a member of a U.S.-trained militia turned his weapon on a third NATO soldier in the east, officials said, the latest in a string of incidents that have undermined trust between allies.

The gunman in the incident in the south started shooting at a group of NATO troops at the entrance of the Provincial Reconstruction Team headquarters in Lashkar Gah, the capital of Helmand province, said Daud Ahmadi, a spokesman for the governor.

A NATO statement said the gunman was killed when some of the foreign forces returned fire. It provided no other details, including the nationalities of the slain service members, but the British Defense Ministry confirmed that they were both British.

Ahmadi said the gunman was a soldier in the Afghan army. A NATO military spokesman said officials were investigating.

In the east, a member of an Afghan Local Police force fatally shot a NATO service member as a group of soldiers approached a checkpoint manned by the militia, the military said in a statement. The incident appeared to mark the first time a member of an ALP group opened fire on foreign troops.

A NATO spokesman said Monday night that he could not say whether the ALP gunman was detained or shot.

So-called “green on blue” shootings have become a rising threat this year, following a series of missteps that have created distrust between Afghan forces and their international coalition partners.

Among the most significant was last month’s burning of Korans by U.S. troops. The episode sparked violent riots and retaliatory attacks, and prompted the Taliban to call on Afghan security forces to open fire on foreign troops.

Since May 2007, at least 80 NATO troops have been killed by Afghan security forces, according to military news releases and statistics provided by the Defense Department to Congress last month. Ten of those killings were committed since the Koran burning.

At a Pentagon press briefing Monday, Gen. John Allen, the top U.S. commander in Afghanistan, said, “In most cases the relationship [between Afghan and NATO forces] is very strong. They know each other well.”

But, he added, “We have taken steps necessary on our side to protect ourselves with respect to, in fact, sleeping arrangements, internal defenses associated with those small bases in which we operate, the posture of our forces, to have someone always overwatching our forces.”

The death of the British troops is likely to further erode support for the war. Publicly, British Prime Minister David Cameron has sounded his determination to stay the course in Afghanistan. But the growing death toll is feeding a decidedly negative sentiment in Britain about the war.

A poll taken in Britain and released this month by ComRes indicated that the percentage of those saying the war is unwinnable has grown from 60 percent last June to 73 percent, with 55 percent saying British troops should be withdrawn immediately, up from 48 percent in June.

Andrew Hawkins, chairman of ComRes, said, “I think we have reached a tipping point that we haven’t had even six months ago where it’s extremely difficult to get the British public behind the war effort” in Afghanistan.

“When Cameron and President Obama stand up and say they want to get troops out as quickly as possible, that’s picked up by voters as meaning ‘we don’t want to be there,’ and if the political leaders don’t want to be there, then they think, ‘let’s get out.’ ”

He said that the British “don’t have a good understanding of the purpose of the mission; they don’t feel the sacrifice of British soldiers is justified by the cause; they don’t think it’s justified given the threat; they don’t think Britain is a safer place.”

Staff writers Karla Adam and Anthony Faiola in London and Craig Whitlock in Washington contributed to this report.