"I think Baghdadi's alive... And I'll believe otherwise when we know we've killed him," Mattis said.
"But, we're going after him. We assume he's alive," he told reporters yesterday.
Last month, the Russian military claimed it had struck a meeting of Baghdadi on May 28 near Raqqa, Syria, in which Baghdadi was possibly killed.
Multiple reports in recent weeks have suggested that Baghdadi was killed in Iraq or Syria. Since making his public appearance as "caliph" in 2014, he has not been seen.
Responding to other questions on Afghanistan, the Pentagon chief said the policy review is not complete yet.
He said he has not used the presidential authorisation to increase the troop number in the war-torn country by 4,000.
"You fight wars for a reason. You don't just fight wars - I'm going to go fight a war now. There's got to be some end state to it, especially when you take a democracy that does not want to go fight wars and have to be able to compel the people to think. Maybe they got their act together here. Maybe this makes sense. So, you come up with a political reason for it," he said.
"Once you get the policy right, then you have to get the strategy right... Because if you don't know where you're going, good luck when you take off on your journey," he said.
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