PENTAGON - Two top U.S. officials are shooting down claims that the leader of the Islamic State terror group is dead.

There have been multiple reports in recent weeks from Russia, Syria, Iran and even from a human rights organization that the Islamic State's self-declared caliph, Abu Bakr al-Baghdadi, was killed in Iraq or Syria.

On Friday, however, both U.S. Defense Secretary Jim Mattis and National Counterterrorism Center Director Nick Rasmussen said there is no proof Baghdadi has been killed.

“I think Baghdadi's alive,” Mattis told Pentagon reporters, adding that despite keeping a low profile, the IS leader likely was still involved in the terror group's decision making.

“We're trying to track him pretty closely,” Mattis said. “He's declared war on us so he's going to reap his reward for it.”

Earlier Friday, Rasmussen said those claiming Baghdadi is dead have yet to produce any sort of proof.

“We know a good bit,” Rasmussen told an audience at an annual security forum in Aspen, Colorado. “I’ve seen nothing that would lead me to believe that the leader of ISIS has been removed from the battlefield.”

Matter of time

Other senior U.S. military leaders say it is likely just a matter of time before Baghdadi is killed.

“We will get him eventually. It's not safe for him on this earth,” U.S. Special Operations Commander Gen. Raymond Thomas said at the security forum in Aspen.

“We've been close,” Thomas said, adding, “Unfortunately, there were some leaks” that caused the leads that his forces had on Baghdadi's whereabouts to dry up.

Thomas specifically referenced some of the reporting on the 2015 raid by U.S. special forces into Eastern Syria that resulted in the death of IS oil minister Abu Sayyaf.

During the raid, the special forces also captured the oil minister's wife, Umm Sayyaf. Thomas said Umm Sayyaf had been traveling with Baghdadi in the week before the raid.

Push-back on rumors

This is the second consecutive week that high-ranking U.S. officials have pushed back against rumors of the IS leader's death.

The commander of the anti-IS coalition in Iraq was the first to dismiss the claims.

"We've heard all kinds of reporting that he's alive, that he's dead," Lt. Gen. Stephen Townsend told Pentagon reporters during a video briefing from Baghdad on July 11. “I don't have a clue. Simple as that.”

Mattis reiterated Townsend's assessment three days later.

“Until we prove it, we don't speculate that he's dead,” Mattis told reporters earlier this month.

Some analysts also have suggested IS leaders have tried to signal to supporters that Baghdadi is still in charge.

“The new issue of Islamic State's weekly publication,al-Naba, contains several references to al-Baghdadi, which are intended to convey he remains alive,” said Michael S. Smith II, a terrorism analyst who specializes in the influence operations of IS and al-Qaida, in an email earlier this week.