KABUL — 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.