“The incident is being investigated as a crime, as such it is clear from a review of the latest available evidence that M’aarek Abu Tayeh was not following Jordanian rules of engagement,” Daoud said. “The formal investigation will make that final determination with certainty.”

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The sudden reversal raises new questions about what led Abu Tayeh to attack a U.S. convoy in broad daylight at a checkpoint at King Faisal Air Base on Nov. 4.

Jordanian officials have called the incident a “tragic misunderstanding” that started after Abu Tayeh heard a loud noise that led him to believe the base was being attacked. After viewing surveillance video of the incident, the slain soldiers’ family members have started employing a different phrase: “cold-blooded murder.”

The incident occurred in a country friendly to the United States, hundreds of miles from the nearest war zone. The men were working for a CIA program to train moderate Syrian fighters when they were killed.

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A military investigation contradicted Jordanian claims, concluding that investigators could find no evidence of a loud noise before Abu Tayeh opened fire. Though an FBI spokesman declined to comment on the matter, Jordanian officials said a joint FBI-Jordanian investigation into the shooting is underway, with the Jordanian portion of the probe “mostly completed.”

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Daoud said Abu Tayeh remains in Jordanian custody.

As recently as last month — in a letter to Rep. Ted Poe (R-Tex.) — Dina Kawar, Jordan’s ambassador to the United States, maintained that Abu Tayeh did follow military rules.

Daoud said that King Abdullah II, responding to requests for an apology from the fathers of the three fallen U.S. soldiers, will be reaching out personally to the family members “to offer his deepest condolences and full support to the investigation.”

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“His majesty’s letters of condolences will be delivered to the families soon,” Daoud said in an emailed statement. “The Ambassador of the Hashemite Kingdom of Jordan to the United States will be reaching out to the families and their representatives in Congress to deliver these letters. The Jordanian government will do everything to ensure that justice is enacted fully.”

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Jim Moriarty, the father of Staff Sgt. James “Jimmy” Moriarty, 27, who was fatally shot by Abu Tayeh, said he hasn’t yet seen the written apology.

The 70-year-old Houston trial lawyer and Marine veteran said that if he ever does see the apology, he no longer intends to accept it. Ever since he viewed surveillance video of the shooting in February, Moriarty has been convinced that his son — as well as Staff Sgt. Matthew Lewellen and Staff Sgt. Kevin McEnroe — were murdered.

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“If the King of Jordan thinks that writing a pious letter saying that he feels really bad that our boys are dead and an investigation is being conducted, that is not going to be nearly enough,” he told The Post. “Any statement that doesn’t include an admission of total guilt and plans for prosecution for the murderer who killed my son and the Jordanians who have failed to do anything about it, will not be enough.”

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“Nobody is going to kill my kid and get away with it,” he added. “I’m going to be chewing on the Jordanian government’s ankles until they are walking on stumps.”

The shooting and aftermath have been a subject of unusual sensitivity for Jordan, a country of 6.5 million that is a close ally to the United States and a key partner in the fight against the Islamic State. Complicating matters for Jordan, the kingdom decided to allow the FBI to take the lead role in investigating the shooting, turning over documents and other evidence to the Justice Department.

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Abdullah discussed the probe with Secretary of State Rex Tillerson during his visit to Amman this month, but Jordanian officials have expressed reluctance in speaking publicly about the possible conclusions of an investigation that is mostly in U.S. hands.

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“It’s hard for them to say very much until they’ve seen the report,” said one U.S. official familiar with the ongoing probe.

Jordanian officials also remain bewildered about the motive for the shooting, according to Jordanian and U.S. officials close to the investigation. No outside group has claimed responsibility, and an extensive inquiry into the gunman’s personal life and social connections turned up no links to terrorist groups or sympathies with jihadist causes, according to officials familiar with probe.

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“This is an embarrassment for the government of Jordan,” said David Schenker, director of the Program on Arab Politics at The Washington Institute for Near East Policy. He added that senior officials in the Jordanian military continue to insinuate that the slain Americans failed to follow procedure despite a lack of evidence, a trend he called “disturbing.”

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“This is a premeditated murder of three Americans by a Jordanian soldier on Jordanian soil and they don’t know what motivated him.”

The killings, which occurred about 150 miles south of the capital, Amman, are believed to be the deadliest single incident involving a CIA team since December 2009, when seven officers and contractors were killed in a suicide bombing in Khost, Afghanistan.

The incident began on the afternoon of Nov. 4 when a four-vehicle convoy carrying U.S. soldiers pulled up to a checkpoint at King Faisal air base. As the convoy waited to enter the base, Abu Tayeh, stationed inside a guard box behind camouflage, opened fire on the second vehicle in the convoy with an M-16 rifle, killing McEnroe and mortally wounding Lewellen, according to a military investigation produced by the Department of Defense.

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“Within seconds of coming under fire, SSG James Moriarty and another soldier exited the third and fourth vehicles in the convoy in order to seek cover as the shooter closed on their position,” the investigation states. “After unsuccessfully trying to communicate to the shooter that they posed no threat, the Soldiers returned fire.”

“While the other soldier maneuvered to gain a better position, SSG Moriarty stood and fired his pistol directly at the shooter, who was wearing body armor,” the investigation adds. “After closing on their position, the shooter shot SSG Moriarty twice mortally wounding him. SSG Moriarty’s actions enabled the remaining soldier to maneuver and engage the shooter and seriously wound him.”

Moriarty said he wanted to believe that the deaths were a case of mistaken identity. But as he watched crisp, color video of the incident inside an FBI field office in Virginia, he said, it was immediately clear to him that the American soldiers were intentionally targeted. The video provides further evidence, he said, that there was no loud noise before Abu Tayeh opened fire.

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What was perhaps most troubling, he said, was that as many as 11 Jordanian soldiers in the vicinity failed to respond after the shooting began, a fact that strikes Moriarty as deeply suspicious.

“I was dumbfounded,” Moriarty, who served in Vietnam, said. “The shooting goes on for six or seven minutes and I’m thinking, ‘Gun battles last 30 seconds, so how does this go on that long and nobody does anything to stop it?’ ”

“Before Jimmy took two shots to the heart, he’s talking and trying to signal that they aren’t a danger. The guard is shooting at Jimmy and another American while they have their arms in the sky — he’s trying to kill them.”

Maj. Gen. James E. Kraft Jr., commander of the Army’s 1st Special Forces Command (Airborne), said Moriarty could have fled the scene of the shooting, but remained at the scene to maintain contact with Abu Tayeh. He referred to the slain soldier as a warrior of “courage, commitment and honor.”

“His actions that day, in the face of grave danger and in the midst of chaos, ensured the safety of his brothers in arms, but ultimately resulted in his death,” he told The Post. “Over the course of their entire history, Army Special Operations Forces (ARSOF) have created a legacy of exceptional commitment to valor, and Staff Sgt. Moriarty will be remembered as a great contributor to that legacy.”

Thomas Gibbons-Neff and Joby Warrick contributed to this report.