In offering the estimate, General Martin Dempsey, chairman of the US Joint Chiefs of Staff, said building up a viable rebel force on the ground would be vital to rolling back the gains of the IS group in Syria -- but warned it would take time and patience.
"We've had estimates anywhere from 12,000 to 15,000 is what we believe they would need to recapture lost territory in eastern Syria," Dempsey told a news conference at the Pentagon.
The current plan for 5,000 recruits to be trained and armed by American instructors over the next year was never intended to represent the total number of troops forming the "moderate" rebel forces.
"Five thousand has never been the end state...," he said.
It was the first time Washington had put a number on how big a rebel force might be required to prevail against the IS extremists in Syria.
The general said defeating the IS group would take more than air power and that "a ground component" was an important aspect of the US-led campaign.
"We believe the path to develop that is the Syrian moderate opposition," he said.
The general said he was "confident" the training effort would be successful but pleaded for patience.
"We have to do it right. Not fast," he said.
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"We need to have military leaders that bind them together. They have to have a political structure into which they can hook, and therefore be responsive to. And that's going to take some time."
The US Congress last week approved President Barack Obama's plan to train and equip up to 5,000 "moderate" rebel troops, and Saudi Arabia has offered to host the training.
Asked who was the head of the opposition that was receiving US assistance, Pentagon Chief Chuck Hagel said there was no leader at the moment as Washington was vetting the recruits.
"We don't have a head of it, in that we are vetting and will continue to vet through our regional partners, State Department, intelligence departments . . .," he said. "We're not going to instruct them as to who their leaders are."
He said a total of 43 US-led air strikes in Syria this week and about 200 in Iraq since August 8 had damaged the IS group but there was a long fight ahead.
"I also want to emphasize that no one is under any illusions -- under any illusions -- that airstrikes alone will destroy ISIL," said Hagel, using an alternative acronym for the group.
"They are one element of our broader comprehensive campaign against ISIL, a campaign that has diplomatic, economic, intelligence and other military components, working with coalition partners and a new government in Iraq."
Hagel also said the cost of the air war for the United States was at about at $7 million to $10 million a day and acknowledged that the Obama administration would have to ask Congress for more funds to cover the operation in coming months.
The US government was still not certain if air attacks in Syria this week had killed senior leaders of the IS outfit or of the Khorsasan group, a collection of Al-Qaeda militants. Dempsey said.
"What we do is, we monitor various kinds of intelligence. We scan social media, which is normally the first place you find out, frankly. But it's too soon to tell," the general said.