Washington (CNN) The U.S. is going to suspend its faltering Syrian rebel training program, U.S. officials said Friday in a move they characterized as a "pause."

"We're going to take an operational pause," Undersecretary of Defense for Policy Christine Wormuth said on a conference call with reporters Friday.

"It's not halting the program," added Brett McGurk, the deputy special envoy for the anti-ISIS effort. "It's adapting it."

Earlier Friday, Defense Secretary Ash Carter said during a news conference in London that the U.S. "remains committed" to training forces in Syria against ISIS, but is looking for ways to "improve" the program.

The New York Times first reported the U.S. move.

The new strategy will shift toward supplying military aid to opposition leaders fighting ISIS instead of training and equipping rebels.

The administration's effort to enhance the moderate Syrian opposition through training and equipment came under heavy scrutiny in recent weeks after the White House acknowledged the program had only succeeded in graduating a handful of recruits, despite spending nearly $500 million on the endeavor.

Administration officials stressed that Syrian rebel commanders would continue to receive military equipment.

"We're going to be providing more basic kinds of equipment to these groups," Wormuth said. "That's how we will mitigate the risk."

Carter said the move was a chance to reassess how to achieve the program's goals.

"I was not satisfied with the early efforts in that regard, and so we are looking at different ways to achieve the same strategic objectives, which is the right one, which is to enable capable motivated forces on the ground to retake territory from ISIL and reclaim Syrian territory from extremism so we have devised a number of different approaches to that going forward," Carter said, using a different name for ISIS.

A U.S. official told CNN that the program is being suspended as the administration looks for other ways to support the moderate opposition in Syria. But U.S. backing for the rebels is not ending.

Pentagon Press Secretary Peter Cook released a statement Friday saying that Carter is now directing the Pentagon to "provide equipment packages and weapons to a select group of vetted leaders and their units so that over time they can make a concerted push into territory still controlled by ISIL."

"We will monitor the progress these groups make and provide them with air support as they take the fight to ISIL," he said.

Cook said "refinements and adjustments" will continue to occur with time, acknowledging that the ISIS fight will be "a long and arduous process."

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The new program will include ammunition and communications equipment for the Syria Arab Coalition, some 5,000 moderate rebels in the north, a U.S. official told CNN.

Current members of the New Syria Force -- the fighters who have been through the train and equip program -- in the field and in training will still get support, though there are not more than a few hundred of them. However, the suspension means that there will be no new recruits or training.

Some U.S. Special Operations commanders had been pressing for that decision for weeks, defense officials told CNN, after seeing the coalition achieve success on the battlefield.

Individuals in the coalition will be vetted through their leadership and given training and be given expertise in communications and intelligence support.

"We have devised a number of different approaches to that going forward and taken them to President (Barack) Obama, and you will be hearing I think very shortly from him," Carter said Friday.

Asked about the news on MSNBC's "Morning Joe" Friday, South Carolina Sen. Lindsey Graham said the program was bound for failure from the start.

"It really is (a joke) because, you have the CIA program and you eventually had a DoD program, the problem with the program is they're training them to fight ISIL only," the GOP presidential candidate said. "No one in Syria is going to just fight ISIL, they want to take Assad on, who has massacred their family, so it was doomed to fail with these restrictions."

Graham has been highly critical of the administration's strategy in Syria and the Middle East more broadly.

Deputy National Security Adviser Ben Rhodes, however, rejected the criticism from some in Congress that the train-and-equip program failed due to a lack of resources and commitment from the administration.

"We didn't expect then and we don't expect now that you can end the conflict in Syria through an opposition group," he told reporters on the conference call.

"I don't think at all that this was a case of poor execution," Wormuth added.

The administration officials on the call said the White House is not currently considering the establishment of a no-fly zone over parts of Syria, one of the key suggestions from critics seeking to bolster the U.S. counter-ISIS campaign and an idea raised recently by Secretary of State John Kerry.

In addition, the officials noted that the President is not contemplating a new policy that would allow Syria's embattled leader Bashar al-Assad to remain in power.

Rhodes argued that the U.S.-led coalition is doing more in its fight against the terror army than Russia has shown in its current intervention into Syria.

"We're actually going after ISIL, which Russia's not doing," Rhodes said.

The officials stressed the campaign to defeat ISIS is not being curtailed, despite the decision to suspend the train-and-equip program.

"We are not ruling out future training," Rhodes added.