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(CNN) —  

Defense Secretary Mark Esper said Tuesday that American troops ordered out of northern Syria will “temporarily” go to Iraq before they return to the US, and that President Donald Trump has not yet approved a plan to keep some troops in Syria to protect oil fields.

“We’re conducting a phased withdrawal – deliberate phased withdrawal from northeast Syria,” Esper told CNN’s Christiane Amanpour in an exclusive interview held at the Prince Sultan Air Base, located in a desert area east of the Saudi capital of Riyadh. “We will temporarily reposition in Iraq pursuant to bringing the troops home. And so it’s just one part of a continuing phase, but eventually those troops are going to come home.”

The Iraqi Joint Operations Command said in a statement Tuesday that US troops withdrawing from Syria may enter the Kurdish region of Iraq and then leave the country, but that they do not have permission to remain in Iraq.

The comments come as Esper leads the removal of US troops from northern Syria, where they had been supporting the SDF. After Trump announced the withdrawal of the troops from the region earlier this month, a move that was met with a strong bipartisan rebuke, Turkey began a widely-anticipated offensive there, which eventually slowed after the US brokered a ceasefire between the two countries last week. On Monday, the secretary said some troops will temporarily remain in Syria to protect oil fields in the country as the Pentagon continues to remove other troops from the country.

“Right now, the President has authorized that some would stay in the southern part of Syria,” Esper said. “And we’re looking maybe keeping some additional forces to ensure that we deny ISIS and others access to these key oil fiends also in middle part of the country, if you will. But that needs to be worked out in time. The President hasn’t approved that yet – I need to take him options sometime here soon.”

Asked by Amanpour who the troops would be securing the oil fields from, Esper responded: “I don’t talk about securing oil fields as much as I talk about denying ISIS access to the oil fields so that they don’t have revenue to continue their bad behavior.”

A US official told CNN on Monday that up to several hundred troops may stay in eastern Syria to protect the oil fields and continue the fight against ISIS. Several hundred additional US troops will also remain at a base in At Tanf in southern Syria, a location near the border with Iraq and Jordan that is seen by many analysts as a curb on Iran’s influence in the region.

“My aim is to keep my options open and really keep the President’s options open, so that as events change on the ground, whether it’s up in northeast Syria or other parts, that we have flexibility to respond to the President’s direction,” Esper said on Tuesday.

Hours before the ceasefire brokered last week is set to run out, Esper told Amanpour that the Kurdish-led Syrian Democratic Forces “are making good faith efforts to withdraw from the area in time” and that “if they need a little bit more time they should be given a little bit more time.”

The secretary said that reports he’s seen in the last day have shown that the ceasefire “is largely holding,” though there “is some skirmishing here and there.”

’We’re not going to go to war with a NATO ally’

Responding to questions about criticism aimed at the US’s decision to withdraw from northern Syria, the secretary said the United States “didn’t sign up to fight a war to defend the Kurds against a longstanding NATO ally.”

He added later that Turkey “is a longstanding NATO ally,” saying, “we’re not going to go to war with a NATO ally and certainly not … with regard to a border that we didn’t sign up to defend in the first place.”

Esper also said that the “11,000 or so” ISIS fighters detained in northeast Syria that some feared would be released when the US troop left the area have mostly remained in prison.

“We’ve only had reports of a little bit more than 100 that have escaped,” he said, adding that the SDF is maintaining guards at the prisons they are in control of.

“So right now we have not seen this big prison break that we all expected, so that’s the good news piece,” Esper said.

Alleged war criminals ‘should be held accountable’

Esper said that he thinks Turkey should be held accountable for alleged war crimes committed by Turkish-backed proxy forces against the Kurds in Syria, allegations that Esper said he assumes are accurate.

“I’ve seen the reports as well, we’re trying to monitor them. They are horrible and if accurate and I assume that they are accurate, they would be war crimes,” Esper said, adding, “I think all of those need to be followed up on. I think those responsible should be held accountable, in many cases it would be the government of Turkey – (it) should be held accountable for this because we cannot allow those things to happen.”

Several US officials have told CNN that they believe the Turkish-backed proxy force that Ankara is using to spearhead its incursion into Syria is comprised of fighters with ties to extremist groups.

Turkey “could have used Turkish regular troops,” a senior US administration official told reporters recently, adding, “Instead they decided to use these thugs and bandits and pirates that should be wiped off the face of the earth.”

Those Turkish-led proxies have been accused by the SDF and others of executing unarmed prisoners, including a civilian Kurdish political leader.

CNN’s Mick Krever, Christie Johnson, Ana Bickford, Darren Bull, Neil Bennett, Hannah Ritchie and Loren Gruenberger contributed to this report.