Libyan forces on Thursday were the verge of driving Islamic State fighters out of their main outpost in the country, but the surprising success of the campaign against Sirte has not eased doubts at the Pentagon that the fledgling government in Tripoli and the Libyan army are cohesive enough to begin new U.S.-led military training and advising operations.

“The Libyan people have a lot of reason themselves to want to get rid of [Islamic State] and it’s clear from what we’re seeing on the ground that they have been successful,” Pentagon spokesman Peter Cook told reporters on Thursday.

U.S. military leaders “are encouraged by the progress we see government forces making and we’ll continue to watch it very closely,” Mr. Cook said of the ongoing Libyan offensive in Sirte against Islamic State.

Fighting under the U.N.-recognized Government of National Accord, Libyan militiamen have nearly secured the costal town, which has been under Islamic State control since November.

On Wednesday, local forces had closed to within three miles of Sirte’s center after weeks of fighting with the backing of heavy air support, the group’s commander, Brig. Gen. Mohammed al-Ghasri, told The Associated Press.

While pockets of the city remain contested, images of Libyan militiamen, mostly from the western city of Misurata, celebrating in the streets of Sirte began circulating through social media site Thursday amid reports of Islamic State militants fleeing their positions throughout the city.

Local forces also had reportedly destroyed the so-called “stage of horror” in the city center, which was the site of gruesome Islamic State executions during the group’s reign in Sirte.

Pentagon officials anticipate the city will fall under the government’s control within days, Col. Chris Garver, the top U.S. military spokesman for anti-Islamic State operations, said Wednesday.

The eventual fall of Sirte is one of several suffered by Islamic State in the region, as the group faces the most serious threat to its Middle East and North African strongholds since the beginning of the U.S.-led coalition’s campaign.

While U.S. military officials were heartened by the rapid success of local forces in Sirte, the only major Islamic State-held territory outside Iraq or Syria, the Pentagon remains on the fence over restarting American-led operations in Libya.

Since the cancellation of a stalled Pentagon program to train and arm Libyan militias, Defense Department officials repeatedly have stated any effort to restart U.S. operations in Libya would depend on the stabilization of the country’s leadership.

While impressive, U.S. military officials still believe the Government of National Accord has not proven they have cleared that bar, Mr. Cook said Thursday.

“There has been no determination” on whether the situation on the ground in Libya warrants a new train and equip operation spearheaded by American forces, based on recent events in Sirte, he said.

“This is an ongoing conversation with a whole host of parties” on what Washington’s next step will be in Libya, Mr. Cook added, noting the one thing that Libyan forces proved in its assault on Sirte is “they can handle this issue on their own.”

Libyan Prime Minister Fayez Seraj echoed that same sentiment before GNA forces launching their assault on Sirte, saying the fractured nation’s own military forces had the wherewithal to take on Islamic State alone.

That said, a small number of U.S. special operations teams have been spotted on the ground in northeast and western Libya for the better part of a year, conducting patrols and advising local militias in the fight against the Islamic State.

Those deployments, coupled with the decision by the Obama administration and its European allies to begin shipping weapons and other equipment to Libya, in the face of U.N. sanctions, were seen by many inside Washington as paving the way for a new train and advise mission in the country.

But Libyan authorities are concerned that the Pentagon’s efforts to arm, train and equip forces may be moving too fast, given the pitfalls of the last U.S.-led effort.

“We have to be cautious. We cannot rush back into this,” Wafa Bugaighis, charge d’affaires at the Embassy of Libya, said during a panel discussion in Washington.

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