The New York Times has asked the Fox News morning show Fox & Friends to apologize for a “malicious and inaccurate segment” about the newspaper, intelligence leaks and Islamic State that aired on Saturday, apparently prompting a critical tweet from Donald Trump.

The Times published a story on Sunday that said Trump was in error when he tweeted on Saturday morning that the “failing” New York Times “foiled” a government attempt to kill Isis leader Abu Bakr al-Baghdadi.

Trump’s full tweet read: “The Failing New York Times foiled US attempt to kill the single most wanted terrorist, Al-Baghdadi. Their sick agenda over national security.”

The Times noted that the Department of Defense issued a news release more than three weeks before the Times article that could have tipped off al-Baghdadi. The paper also said the Pentagon “raised no objections” with it before the 2015 article on the intelligence gleaned from the raid was published.

Times spokeswoman Danielle Rhoades Ha said she had requested an “on-air apology and tweet” from Fox & Friends.

The Fox & Friends segment in question referred to comments by Gen Tony Thomas, the head of US special operations command, who said his team was “close” to al-Baghdadi after a 2015 raid but the “lead went dead” after it “was leaked in a prominent national newspaper”.

The Times, Rhoades Ha wrote, took issue with a Fox & Friends host saying al-Baghdadi “was able to sneak away under the cover of darkness after a New York Times story” in 2015, and a host’s comment that the US government “would have had al-Baghdadi based on the intelligence that we had except someone leaked information to the failing New York Times”.

The Fox story said Thomas “appeared to be referring to a New York Times report in June 2015 that detailed how American intelligence agencies had ‘extracted valuable information”’.

(UPDATED) U.S. General: Leak let ISIS leader slip away pic.twitter.com/wNJgQqOK1b — FOX & friends (@foxandfriends) July 24, 2017

On Monday, Fox & Friends host Steve Doocy replayed Thomas’s comments and noted that the Times had published its explanation, directing viewers to the newspaper’s statement, posted on Foxnews.com. He did not apologise.

