The New York Times says Fox News hasn't addressed what the Times called its "sheer hypocrisy" after the network aired a report suggesting the paper had inadvertently helped ISIS' leader.

The Times on Sunday called on the cable news network to amend what it termed a "malicious and inaccurate" report that put the newspaper at fault for allowing ISIS chief Abu Bakr al-Baghdadi to escape capture in 2015.

Although Fox News has updated its reporting -- which was based on comments recently made by a U.S. general -- with a statement from the Times, it has not apologized for any part of its story.

"For all of their hyperventilating to the media about a correction, the New York Times didn't reach out to anyone at Fox News until Sunday afternoon for a story that ran Friday night," a spokesperson for the network told CNNMoney.

A Fox News host over the weekend blamed the Times for publishing information from a military raid in Syria; the publication of that information, a U.S. general claimed recently, thwarted an attempt to find Baghdadi.

The Times story in question was published weeks after news of the raid was first made public. The paper noted Monday, however, that the raid was not only publicized by the Pentagon after it happened, but was also widely covered in the media -- including by Fox News.

"According to the curious logic of the Fox & Friends host, Fox News itself was unpatriotic," the Times said in its statement Monday.

In a statement Monday evening, a Fox News spokesperson hit back, saying, "Neither Fox News' report nor the subsequent on-air coverage was inaccurate. We find it beyond disappointing that the New York Times, in an attempt to distract from their recent debacle, decided to blame Fox News for comments made publicly by General Thomas during a widely viewed panel at the Aspen Security Forum. It might behoove the Times to actually check in with their reporter Eric Schmitt to see whether Gen. Thomas' comments have merit and whether Schmitt's reporting in 2015 revealed intelligence that allowed ISIS leader Abu Bakr al-Baghdadi to slip away."

Fox News first mentioned the controversy in an article that ran on its website late Friday. The story attracted widespread attention Saturday when it was mentioned on the morning TV show "Fox & Friends" and apparently from there picked up by President Trump.

The story was referenced on the program at 6:19 a.m. Saturday. About 25 minutes later, Trump -- a frequent "Fox & Friends" viewer -- tweeted about the report and accused the "Failing New York Times" of having a "sick agenda over National Security."

The Failing New York Times foiled U.S. attempt to kill the single most wanted terrorist,Al-Baghdadi.Their sick agenda over National Security — Donald J. Trump (@realDonaldTrump) July 22, 2017

That tweet gave Fox News fodder to return to the story later in the day. After referencing Trump's tweet, co-host Clayton Morris claimed that Baghdadi "was able to sneak away under the cover of darkness after a New York Times story."

"It's not just failing in its credibility," co-host Pete Hegseth said of the Times during that segment. "It's failing our country."

On Sunday, the Times pushed back. It published a lengthy fact check that refuted Trump's tweet and the Fox News story. The paper also wrote a letter to the executive producer of "Fox & Friends" to demand an apology.

"With this segment, Fox & Friends demonstrated what little regard it has for reporting facts," the letter read.

Fox News updated its website Sunday with a statement from the Times. Weekday co-host Steve Doocy also read part of the statement on air Monday.

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

After Doocy's remarks aired, a Times spokesperson told CNNMoney that the segment "wasn't an apology, nor did it begin to address the larger issues with the Fox & Friends Weekend segment, one of which was sheer hypocrisy."

The network's online report was apparently based on comments made last week by U.S. Army General Tony Thomas, who is in charge of Special Operations Command.

Thomas said at a security forum in Aspen, Colorado that officials were close to catching al-Baghdadi after a 2015 raid that killed another ISIS leader, Abu Sayyaf. The raid led to the capture of Abu Sayyaf's wife, Umm Sayyaf, and some documents.

Thomas called information gleaned from the raid a "very good lead," but he said it "went dead" after it was "leaked to a prominent national newspaper," according to Fox News.

In its Friday article, Fox News said that Thomas appeared to be talking about a Times report published in June 2015 that described how U.S. intelligence agencies "extracted valuable information" during the raid.

The Times in its responses Sunday outlined the timeline of events that led it to publish its story.

Here's the letter the @nytimes sent the exec producer of "Fox & Friends Weekend" requesting apology for "malicious and inaccurate segment" pic.twitter.com/s1oz7rzeLN — Oliver Darcy (@oliverdarcy) July 23, 2017

The Pentagon publicly announced the raid, the death of Abu Sayyaf, and the capture of Umm Sayyaf, on May 16, 2015, the Times noted. Several media outlets reported about it at the time, including the Times and Fox News.

More than three weeks later, the Times published another story about the raid that included new details about how Baghdadi tried to avoid American forces.

The Times said the gap between when the raid became public and when it published its June story is critical. Baghdadi would have known about the raid from either his own sources, the Pentagon statement or the media reports that came immediately afterward, the Times contended.

"If the U.S. government wanted to keep the detention and likely interrogation of the wife secret, the Pentagon would not have publicly announced it," the Times said in its letter to Fox News.

The newspaper said that before it published the story, it described the piece to the Pentagon, which did not object to the details. The Times also said that "no senior American official complained publicly about the story until now, more than two years later."

In its letter to Fox News, the Times also said the network did not reach out the paper for comment.

--CNNMoney's Oliver Darcy contributed to this story.