The statement did not mention the targeting of any individuals.

Syrian activists also reported the strikes, saying that they had killed at least two children and an unknown number of fighters.

One hit a car belonging to the Nusra Front in the village of Sarmada. The activists did not say who had been in it.

Other strikes hit facilities belonging to the Nusra Front in the town of Harim, reducing them to rubble, and a base belonging to another Islamist rebel group, Ahrar al-Sham, near a border crossing with Turkey. In statements and photos posted online, Ahrar al-Sham and the Nusra Front acknowledged that their bases had been hit, and the Nusra Front released photos on Twitter that it said showed dead civilians.

The Syrian Observatory for Human Rights, an antigovernment monitoring group, said that two young girls had been killed in the strike on Harim and that six members of the Nusra Front had been killed in another strike in Aleppo Province farther east. Another activist, who gave his name as Ibrahim al-Idlibi, said seven civilians had been killed in addition to a number of fighters from Ahrar al-Sham.

A spokesman for the Department of Defense, Col. Steven H. Warren, said that Syria was an “extremely complex operating environment” and that the United States took precautions to prevent civilian casualties.

Many in the Syrian opposition have expressed skepticism about the existence of the Khorasan group, saying that the United States had created it to justify strikes on Islamist rebels. Some also defend the Nusra Front, calling it a loyal ally in the fight against President Bashar al-Assad.

All the strikes on Tuesday occurred in the ungoverned strip of land along the Turkish border, where many rebel groups have bases and frequently go to Turkey to buy supplies and to take a break from the war. Membership in many of these groups is fluid, with fighters flowing among them based on who has arms and money.

The United States has been providing limited arms support to a small number of rebel groups deemed to be moderates, and a larger effort to train 5,000 rebels a year to fight the Islamic State is in the planning stages.