(CNN) A spy for Kurdish forces in Syria stole Abu Bakr al-Baghdadi's underwear in order to obtain a DNA sample of the ISIS leader and help lead the US military to his location, Kurdish officials have claimed.

Officials from the Kurdish-led Syrian Democratic Forces (SDF) described how they tracked the elusive Baghdadi from one end of Syria to the other in the months leading up to this weekend's operation which left the world's most wanted terrorist dead.

"Through our own sources, we managed to confirm that Al Baghdadi had moved from Al Dashisha area in [Deir Ezzor] to Idlib. Since 15 May, we have been working together with the CIA to track Al Baghdadi and monitor him closely," Polat Can, a senior adviser for the SDF, tweeted on Monday.

Mustafa Bali, a spokesman for the SDF, confirmed Can's account, telling CNN that an informant had obtained Baghdadi's underwear and a blood sample that was used for the DNA test which confirmed his identity before the raid took place.

CNN could not confirm the Kurds' claim, but their cooperation with the US in the runup to the Baghdadi raid took place as the Trump administration was abandoning the SDF in northern Syria.

Baghdadi "blew himself up" after he was cornered by US forces during a daring, two-hour nighttime assault on his compound in Idlib, northern Syria on Saturday, US President Donald Trump announced on Sunday.

A senior State Department official told reporters Monday that the SDF "played a key role" in the Baghdadi raid, and that the US has been "in close touch" with SDF Commander Gen. Mazloum Abdi "about all aspects of what we're doing."

"He, his people, and his intelligence sources, played a key role in all of this," the official said. "It's a very, very important role. Nobody should underestimate how key the SDF was in all of this."

Earlier this week, Mazloum said there had been five months of "joint intel cooperation on the ground" leading up to the raid. The State Department official said Mazloum's statements about the raid were accurate.

SDF spokesperson Kino Gabriel told CNN that Trump's surprise withdrawal of US troops from parts of northern Syria in early October delayed the operation to kill Baghdadi. Kurdish groups said they considered the US pullback -- which led to a Turkish offensive to clear Kurdish forces from the Syrian border area -- a "betrayal."

source with knowledge of the subject told CNN that Trump's controversial order to withdraw US troops from Syria in mid-October had a major impact on the planning of the Baghdadi operation, but did not necessarily accelerate its launch.

The official also said that the operation would have been impossible without US troops in Syria and the partnership with the SDF.

Baghdadi's death marked the end of a years-long hunt to find one of the most wanted terrorists in the world and the man who declared a so-called Islamic caliphate in Iraq and Syria in 2014.

It was the most significant announcement of the death of a terror leader since President Barack Obama revealed al-Qaeda leader Osama bin Laden had been killed by US Navy Seals in a dramatic late night address in May 2011.