"The Failing New York Times foiled USA attempt to kill the single most wanted terrorist", Trump tweeted, referring to Abu Bakr al-Baghdadi.
Russia's army said in mid-June that it was seeking to verify whether it had killed the ISIL chief in a May airstrike in Syria.
But US defence secretary General James Mattis said on Friday: "I think Baghdadi's alive. and I'll believe otherwise when we know we've killed him. That's a challenge we have in terms of where and how our tactics and procedures are discussed openly", said Thomas. American officials expressed confidence that an influential lieutenant, Abu Hamid, was killed in the attack, but the Islamic State, which remains resilient, has not yet confirmed his death.
In a 2015 raid ISIS oil minister Abu Sayyaf was killed and the United States obtained a great deal of "valuable information" about ISIS' structure and methods of evasion. The Syrian city is the terror group's de facto capital in Syria. The US intelligence community has also seen no evidence Baghdadi is dead.
"At one point, we were anxious about this out-rush, outflows, massive outflows of foreign fighters once the battlefield situation changed in Iraq and Syria and that Western countries, countries in the region, would be flooded with returnees", he said.
USA officials have repeatedly challenged that claim, but have not been able to prove he is still alive. The article shared information about al-Baghdadi's operations and his attempts to avoid capture by USA forces, and quoted several high-ranking American officials, including a statement from an unnamed top senior State Department official, who told the newspaper: "Every single day the picture becomes clearer of what this organization is, how sophisticated it is, how global it is and how networked it is".
While there may be no major outflow of foreign fighters, Rasmussen said he is concerned by the threat posed by Islamic State's affiliates from Asia to Africa.
Trump supporters meanwhile, back the president's attempts to stick it to the so-called mainstream media who are pursuing a "witch hunt" against him.