WASHINGTON – CIA operatives and U.S. special operations troops have been secretly training Syrian rebels with antitank and antiaircraft weapons since late last year, months before President Obama approved plans to begin directly arming them, according to U.S. officials and rebel commanders.

The covert U.S. training at bases in Jordan and Turkey, along with Obama’s decision this month to supply arms and ammunition to the rebels, has raised hopes among the beleaguered Syrian opposition that Washington ultimately will provide heavier weapons as well. So far, the rebels say they lack the weapons they need to regain the offensive in the country’s bitter civil war.

The tightly constrained U.S. effort reflects Obama’s continuing doubts about being drawn into a conflict that has already killed more than 100,000 people and his administration’s fear that Islamic militants now leading the war against President Bashar Assad could gain control of advanced U.S. weaponry.

The training has involved fighters from the Free Syrian Army, a loose confederation of rebel groups that the Obama administration has promised to back with expanded military assistance, said a U.S. official, who discussed the effort anonymously because he was not authorized to disclose details.

The number of rebels given U.S. instruction in Jordan and Turkey could not be determined, but in Jordan, the training involves 20 to 45 insurgents at a time, a rebel commander said.

U.S. special operations teams selected the trainees over the last year when the U.S. military set up regional supply lines to provide the rebels with nonlethal assistance, including uniforms, radios and medical aid.

The two-week courses include training with Russian-designed 14.5-millimeter antitank rifles, antitank missiles and 23-millimeter antiaircraft weapons, according to a rebel commander in the Syrian province of Dara who helps oversee weapons acquisitions and who asked that his name not be used because the program is secret.

The training began in November at a new American base in the desert in southwestern Jordan, he said. So far, about 100 rebels from Dara have attended four courses, and rebels from Damascus, the Syrian capital, have attended three, he said.

“Those from the CIA, we would sit and talk with them during breaks from training, and afterward they would try to get information on the situation inside” Syria, he said.

The rebels were promised enough armor-piercing antitank weapons and other arms to gain a military advantage over Assad’s better-equipped army and security forces, the Dara commander said. But arms shipments from Qatar, Saudi Arabia and other Arab countries, provided with assent from the Americans, took months to arrive and included less than the rebels had expected.

Since last year, the weapons sent through the Dara rebel military council have included four or five Russian-made heavy Concourse antitank missiles, 18 14.5-millimeter guns mounted on the backs of pickup trucks and 30 82-millimeter recoil-less rifles. The weapons are all Soviet or Russian models but manufactured in other countries, the commander said. Such weapons allow the rebels to easily use captured munitions from the Syrian army, which has a large arsenal of Russian and Soviet arms.

“I’m telling you, this amount of weapons, once they are spread across the province (of Dara), is considered nothing,” the commander said. “We need more than this to tip the balance or for there to even be a balance of power.”