Four U.S. troops were killed Sunday at a remote checkpoint in southern Afghanistan when a member of the Afghan security forces opened fire on them, military officials said. The attack brought to 51 the number of international troops shot dead by their Afghan partners this year.

The insider attack came on the same day that NATO warplanes killed nine women gathering firewood in the mountains outside their village in an eastern province, according to local officials, adding to long-festering outrage here over civilian casualties. Although the coalition said it regretted any civilian deaths, the incident was likely to further strain relations between Afghans and the international forces.

The weekend’s events touched the core of the U.S.-led war’s problems. The escalating insider ­attacks and continuing civilian casualties both deepen mistrust and alienate NATO forces from the people they are supposed to be protecting, undermining an already fragile partnership.

The Americans and their coalition partners are training Afghan forces to take over responsibility for the nation’s security and enable the United States to pull out its combat troops by the end of 2014.

The American troops were killed Sunday near a NATO installation in Zabul province, at a checkpoint staffed by both foreign and Afghan forces. (The United States did not immediately release information on which service branch the troops belonged to.)

On Saturday, an Afghan gunman thought to belong to the local police killed two British soldiers in southern Helmand province.

The weekend killings marked an escalation of insider attacks on international troops here that coincided with Muslim rage worldwide that was sparked by a video that defames the Islamic prophet Muhammad. It was unclear, however, whether the shootings were connected to the video, “Innocence of Muslims,” snippets of which can be seen on the Internet.

Even so, the inflammatory video and insider killings have had a significant impact on U.S. military and Afghan army operations in some areas during the past three days. Top NATO officers ordered their field commanders to conduct risk assessments and determine whether to postpone or scale back some missions in response to the recent Afghan anger.

In Wardak province, a restive area south of Kabul, some commanders appeared to misinterpret the guidance and postponed several major operations for three days. Because Afghan army commanders in Wardak were reluctant to patrol without support from U.S. troops, they also chose to cancel the planned missions.

The pause in Wardak had initially been planned to last only two days, but U.S. commanders extended it in the immediate aftermath of a Friday night attack by the Taliban on Camp Bastion — a large British base in Helmand province — so that U.S. troops could focus on internal base security in case similar insider attacks were launched.

The Taliban said the attack on Camp Bastion, which is hundreds of miles from Wardak, was initiated to avenge the video and to target Britain’s Prince Harry, a helicopter gunner on the base. Two U.S. Marines died in the attack, and upwards of $200 million in aircraft and base structures were destroyed.

Col. Thomas Collins, a spokesman for the NATO-backed International Security Assistance Force, confirmed the pause in some operations but said such readjustments are not unusual.

“Recent events outside of and inside Afghanistan related to the ‘Innocence of Muslims’ video plus the conduct of recent insider attacks have given cause for ISAF troops to exercise increased vigilance and carefully review all activities and interactions with the local population,” Collins said in a statement.

Shooter is killed

The latest fatal insider attacks on U.S. troops involved a group of Afghans wearing the uniforms of the Afghan National Police — a component of the country’s 352,000-member security forces. Jailani Khan Farahi, a senior police officer for Zabul province, said the assassin was a member of that force and worked closely with foreign troops in the area.

The shooter was killed in reciprocal firing, and five of his colleagues fled, Farahi said. It was unclear whether the five were also involved in the killings.

In a statement on its Web site Sunday, the Taliban said four Americans died, crediting “one Afghan mujahed,” or holy warrior, for carrying out the attack.

NATO and Afghan officials have undertaken intense efforts recently to prevent insider attacks. The Afghans say they have been weeding out potential turncoats and Taliban infiltrators through better screening. They also have increased counterintelligence operations in the ranks and introduced cultural sensitivity training so that Afghan forces can better understand Western behaviors.

Taliban infiltrators are estimated to account for 25 percent of the insider attacks, with the rest attributed to Afghans who are settling personal scores, avenging perceived humiliations or making larger statements against the international troop presence — including civilian casualties.

Airstrikes in mountains

Sunday’s NATO airstrikes in the mountains of eastern Laghman province further fueled anger among Afghans — including President Hamid Karzai, who condemned the killings. The U.S.-led international coalition said the precision strikes killed “a large number of insurgents” but also acknowledged that up to eight civilians had been hit.

Chanting “Death to America,” protesters deposited what local authorities said were the bodies of nine victims at the residence of the provincial governor, about 30 miles from where the strikes occurred. Seven other women and girls were reported to be injured.

“We strongly condemn it — killing innocent women is not justifiable at all,” said Alif Shah, governor of the province’s Alingar district. “The operation was not coordinated with the Afghan authorities.”

Douglas Ollivant, a fellow at the New America Foundation and former National Security Council official, said that such incidents contribute to insider attacks but that he thinks “the root cause is the perceived disrespect the Afghans get from their NATO allies and trainers.”

As for the video, he said, “it probably isn’t going to set you off if your honor isn’t already being bruised.”

Lt. Col. Hagen Messer, a coalition spokesman, said there was no evidence to suggest that the two insider attacks in two days had a connection to the controversial video, which has provoked protests and violence in some 20 countries.

“Every one of these insider attacks is handled as its own individual incident,” Messer said. “We can’t draw the conclusion that there is a single reason or point.”

Since 2007, when the insider- attack phenomenon began, about 109 international troops have been killed by rogue Afghan security forces.

Last week, the Taliban called for increased attacks in Afghanistan, specifically on U.S. forces, to avenge the video as well as “all the violations against our heavenly book,” the Koran, and the prophet Muhammad.

“The mujaheddin in Afghanistan should avenge these actions of the American government by dealing a heavy blow to its invading troops on the battlefield,” an official Taliban Web site said.

Jaffe reported from Jaghatu, Afghanistan. Javed Hamdard and Sayed Salahuddin in Kabul contributed to this report.