The U.S. military program to train so-called moderate Syrian rebels in Turkey and Jordan to fight ISIS has run into a number of difficulties that are slowing the effort down, Pentagon officials now openly acknowledge.

Of the 6,000 Syrians who have volunteered to be part of the program, less than 200 have begun training.

One of the factors causing the problems, according to Pentagon spokesman Col. Steven Warren, has been the “exfiltration” of qualified fighters from Syria – the very risky process of getting them out of Syria to the training sites. None of those at the training sites has yet completed the program.

READ: Carter, Dempsey paint bleak picture of Iraq situation

The Pentagon effort was aimed at bringing rebels fighters not associated with ISIS or Al Qaeda affiliates out of Syria and then training them in skills they could use to go back home and defend their areas against ISIS.

The hope was that this effort would train significantly larger numbers of fighters than a longstanding covert effort by the CIA to train rebels.

Of the 6,000 rebels who volunteered to be in the Defense Department program, some 4,000 are still waiting to be fully vetted by the U.S. Part of the process is getting assurances the fighters, once they’ve gone through training, will return to their towns and villages to fight ISIS rather than the Assad regime. Some 1,500 of the 6,000 have passed through the vetting process, while about 500 have been turned down for a variety of reasons.

The U.S. plan had been to train about 3,000 during the rest of 2015 and about 5,400 every 12 months after that.

“The Syria train-and-equip program is even more challenging than the Iraq train-and-equip program,” Defense Secretary Ashton Carter told the House Armed Services Committee Wednesday.

U.S. Army Apache helicopters, like the one pictured here, have been used to support Iraqi troops in their fight against ISIS. Click through the gallery to see what other military assets the Pentagon has put into the ISIS battle.

The workhorses of the American fighter fleet, F-16s, have been used in dozens of strikes against ISIS. F-16s can travel 1,500 mph, or Mach 2, at altitude.

A F-15E Strike Eagle from the 391st Fighter Squadron takes off in July during a mission at Joint Base Pearl Harbor-Hickam in Hawaii. The F-15E Strike Eagle can carry more than 23,000 pounds of payload for air-to-ground and air-to-air combat. The plane has been in the Air Force inventory for three decades and is expected to be operational until at least 2035.

The A-10 Thunderbolt II, also known as the Warthog, joined the fight against ISIS in late 2014. The jets are specially designed for close air support of ground forces.

U.S. Air Force F-22 Raptors saw their first combat during strikes on ISIS targets in Syria, the Pentagon said. The single-seat, twin-engine stealth fighter has a top speed of almost 1,500 mph. Here, a Raptor performs during the Australian International Airshow in March 2013.

The Air Force's B-1B Lancer bomber was introduced in the 1980s to carry out nuclear missions. The plane was adapted for conventional weapons missions in the 1990s and has flown in combat over Iraq, Kosovo and Afghanistan. Here a B-1B flies above Iraq in support of Operation New Dawn in February 2011.

F/A-18 jets and other aircraft used in strikes against ISIS have been launched from Navy carriers, including the the USS George H.W. Bush, a 103,600-ton aircraft carrier seen here in April as it transits the Strait of Hormuz.

EA-6B Prowlers are among the U.S. aircraft that took off from the USS George H.W. Bush during attacks on ISIS. The Prowler is used to support attack aircraft by jamming enemy radar and communications and obtaining tactical intelligence. Here, a Prowler -- seen at bottom -- flies in formation with an E-2C Hawkeye in June 2004.

The guided-missile cruiser USS Philippine Sea, operating in international waters in the North Arabian Gulf, launched Tomahawk cruise missiles used against ISIS targets in Syria in some of the initial strikes on ISIS. The ship has a displacement of 9,589 tons and carries a crew of 370.

On September 22, 2014, the United States fired 47 Tomahawk missiles against targets in Syria. Tomahawks are long-range subsonic cruise missiles used to take out high-value or heavily defended land targets. They were first used in Operation Desert Storm in 1991. Here, the U.S. Navy guided-missile destroyer USS Barry (DDG 52) launches a Tomahawk cruise missile in 2011.

The guided-missile destroyer USS Arleigh Burke, operating in the Red Sea, launched Tomahawk cruise missiles against ISIS targets in the first of three waves of attacks that began on September 22. The ship has a displacement of 8,373 tons and carries a crew of 370. It is part of the U.S. 5th Fleet.

U.S. military assets used against ISIS

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“We are trying to recruit and identify people that … can be counted on – that is, to fight, to have the right mindset and ideology,” Carter said, emphasizing fighters could not be aligned with groups like ISIS and must be willing to take actions to fight ISIS.

“It turns out to be very hard to identify people who meet both of those criteria,” he said.

The U.S. is also still struggling to decide what responsibility it will take for these fighters once they are sent back to their homes in Syria to fight ISIS.

“I believe we have some obligation to support them and protect them, including supply them,” Carter said, adding that he is aware that there are concerns that weapons provided during training could be “diverted.”

“These constraints that we put on ourselves, which are perfectly understandable, do progressively limit the number of inductees into the program,” he said. “And that’s proving (to be) the thing that limits the growth of the program. We have enough training sites and so forth for them. For now, we don’t have enough trainees to fill them.”

This comes at a time when the Assad regime may be under the greatest strain to maintain its power because of both ISIS’s ability to take territory and gains made by rebels groups.

READ: House votes to keep U.S. troops deployed against ISIS

At the same hearing, Gen. Martin Dempsey, chairman of the Joint Chiefs of Staff, revealed that that very subject came up in discussions during his recent trip to Israel to meet with top military officials there.

“That was the purpose of my trip to the region, actually, was to discuss with regional partners a scenario in which the regime would either collapse,” he said, or Assad “would depart for one reason or another.

Dempsey said that nations in the region believe the most likely near-term scenario is the Assad regime could go on the defensive “and limit its protection of the Alawite Shiite and some of the minority groups, leaving the rest of Syria essentially ungoverned, or governed in ways that … wouldn’t be positive for the region in the near term.”

U.S. defense officials told CNN that all of Syria’s bordering countries, including Israel, Turkey, Jordan and Lebanon are concerned that a precipitous collapse of the Assad regime could lead to a security and refugee crisis on their borders.

U.S. intelligence officials have noted for the last couple of months that Assad’s forces have appeared increasingly exhausted, units are undermanned and in some cases the regime may not be paying its bills to weapons suppliers in Russia.