KABUL, Afghanistan – 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 film that defames the Islamic prophet Muhammad. It was unclear, however, whether the shootings were connected to the unreleased “Innocence of Muslims” movie, snippets of which can be seen on the Internet.

Even so, the movie, along with 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, south of Kabul, some commanders appeared to misinterpret the guidance and postponed several major operations for three days. Because Afghan army commanders in Wardak Province were reluctant to patrol without support from U.S. troops, they also chose to cancel the planned missions.

The pause in Wardak Province had initially been planned for 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 Province, was initiated to avenge the Islam-insulting movie and also meant 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.

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 gunman was killed in reciprocal firing and five of his colleagues fled, Farahi said.

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

NATO and Afghan officials have undertaken intense efforts to prevent insider attacks. The Afghans say they have been weeding out potential turncoats and Taliban infiltrators through better screening. They also have increased counter-intelligence 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.

Sunday’s NATO airstrikes in the mountains of eastern Laghman province fueled further 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 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, district governor of the province’s Alingar District. “The operation was not coordinated with the Afghan authorities.”

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