Appearing on NBC's "Today" show, an unshaven Engel said he and his team escaped during a firefight Monday night between their captors and rebels at a checkpoint. They crossed into Turkey on Tuesday.
NBC did not say how many people were kidnapped with Engel, although two other men, producer Ghazi Balkiz and photographer John Kooistra, appeared with him on the "Today" show. It was not immediately clear whether everyone was accounted for.
Engel said he believes the kidnappers were a Shiite militia group loyal to the Syrian government, which has lost control over swaths of the country's north and is increasingly on the defensive in a civil war that has killed 40,000 people since March 2011.
"They kept us blindfolded, bound," said the 39-year-old Engel, who speaks and reads Arabic. "We weren't physically beaten or tortured. A lot of psychological torture, threats of being killed. They made us choose which one of us would be shot first and when we refused, there were mock shootings," he added.
"They were talking openly about their loyalty to the government," Engel said. He said the captors were trained by the Iranian Revolutionary Guard and allied with Hezbollah, the Lebanese Shiite militant group, but he did not elaborate.
There was no mention of the kidnapping by Syria's state-run news agency.
Both Iran and Hezbollah are close allies of the embattled Syrian government of President Bashar Assad, who used military force to crush mostly peaceful protests against his regime. The crackdown on protests led many in Syria to take up arms against the government, and the conflict has become a civil war.
Engel said he was told the kidnappers wanted to exchange him and his crew for four Iranian and two Lebanese prisoners being held by the rebels.
"They captured us in order to carry out this exchange," he said.
Engel and his crew entered Syria on Thursday and were driving through what they thought was rebel-controlled territory when "a group of gunmen just literally jumped out of the trees and bushes on the side of the road."
"There were probably 15 gunmen. They were wearing ski masks. They were heavily armed. They dragged us out of the car," he said.
He said the gunmen shot and killed at least one of their rebel escorts on the spot and took the hostages into a waiting truck nearby.
Around 11 p.m. Monday, Engel said he and the others were being moved to another location in northern Idlib province.
"And as we were moving along the road, the kidnappers came across a rebel checkpoint, something they hadn't expected. We were in the back of what you would think of as a minivan," he said. "The kidnappers saw this checkpoint and started a gunfight with it. Two of the kidnappers were killed. We climbed out of the vehicle and the rebels took us. We spent the night with them."
Engel and his crew crossed back into neighbouring Turkey on Tuesday.
The network said there was no claim of responsibility, no contact with the captors and no request for ransom during the time the crew was missing.
NBC sought to keep the disappearance of Engel and the crew secret for several days while it investigated what happened to them. Major media organizations, including The Associated Press, adhered to a request from the network to refrain from reporting on the issue out of concern it could make the dangers to the captives worse. News of the disappearance did begin to leak out in Turkish media and on some websites on Monday.
Syria has become a danger zone for reporters since the conflict began.
According to the Committee to Protect Journalists, Syria is by far the deadliest country for the press in 2012, with 28 journalists killed in combat or targeted for murder by government or opposition forces.
Among the journalists killed while covering Syria are award-winning French TV reporter Gilles Jacquier, photographer Remi Ochlik and Britain's Sunday Times correspondent Marie Colvin. Also, Anthony Shadid, a correspondent for The New York Times, died after an apparent asthma attack while on assignment in Syria.
The Syrian government has barred most foreign media coverage of the civil war in Syria. Those journalists whom the regime has allowed in are tightly controlled in their movements by Information Ministry minders. Many foreign journalists sneak into Syria illegally with the help of smugglers and travel with rebel escorts or drivers.
Engel joined NBC in 2003 and was named chief foreign correspondent in 2008. He previously worked as a freelance journalist for ABC News, including during the U.S. invasion of Iraq. He has lived in the Middle East since graduating from Stanford University in 1996.