A Trump Organization attorney suggested Monday night that Donald Trump might sue the New York Times over a Sunday front page story about his behavior around women.

Then on Tuesday morning, another Trump attorney said "I don't think that this is going to end up in litigation," but called on The Times to retract the story and apologize.

The newspaper will not be doing that. It is standing firmly behind the story, which was the product of weeks of intensive reporting.

The controversy is the latest illustration of how Trump runs against the media while simultaneously courting media attention.

The presumptive GOP nominee tweeted 14 times on Monday, and 10 of the messages were broadsides against the Times. Among other things, he said the "failing" newspaper published a "false, malicious and libelous story" that was "totally dishonest."

The denunciations rallied Trump's supporters to his side while driving more traffic to the Times web site. The story ranked #1 on the Times' lists of most popular and most shared articles -- even though it was a day old and was hard to find on the Times home page.

A Times spokeswoman said the article is the news organization's most read politics story of the year, according to internal metrics.

Michael Barbaro and Megan Twohey's reporting, including 50-plus interviews, revealed examples of "unwelcome advances, a shrewd reliance on ambition, and unsettling workplace conduct over decades."

Trump began criticizing the story on Sunday morning, declaring that it was "a lame hit piece" and "a joke."

Later in the day he asked, "Why doesn't the failing @nytimes write the real story on the Clintons and women? The media is TOTALLY dishonest!"

He kept up the critique on Monday morning. He seized on a Fox interview with the first woman mentioned in the story, former girlfriend Rowanne Brewer Lane, who said the Times "spun" her words to make them seem negative.

Brewer Lane did not dispute any of the specific quotes or ask for a correction. But her complaint -- repeated on CNN later on Monday morning -- was enough for Trump to claim that the story was a "fraud."

He called up CNN's "New Day" control room to point out the Fox interview. And he tweeted, inaccurately, that the whole story has been "proven false." He also told his Twitter followers that nothing in the newspaper could be trusted: "Who can believe what they write after the false, malicious & libelous story they did on me."

Trump's use of the word libelous stood out to some observers since Trump has talked repeatedly about wanting to "open up the libel laws" to make it easier to sue media companies.

The candidate didn't tweet a lawsuit threat, but Trump Organization assistant general counsel Jill Martin left one on the table when asked about it on CNN's "Erin Burnett OutFront" Monday night.

"I think that is a distinct possibility," Martin said. "I haven't talked to him about it personally, but, you know, when he's attacked like that and things are said falsely, he definitely fires back."

Trump does have a reputation for being litigious, but he also has a reputation for blustery rhetoric about lawsuits that don't result in actual suits.

During a Tuesday morning interview on CNN, Trump Organization general counsel Michael Cohen agreed with anchor Chris Cuomo's statement that there's a "very high bar" for suing news organizations.

"It's a very high bar," Cohen said. "I don't think that this is going to end up in litigation. The truth is that The New York Times owes both Ms. Brewer and they owe Donald Trump an apology."

Cohen added, "They need to do a retraction and they need to actually be fair, because they're destroying their paper."

What surprised some people at the Times was the Trump camp's decision to repeatedly draw more attention to Barbaro and Twohey's reporting.

@brianstelter But in all seriousness, when was last time a major party nominee spent day making sure MORE people saw story they disliked? — Maggie Haberman (@maggieNYT) May 17, 2016

"In all seriousness, when was last time a major party nominee spent day making sure MORE people saw story they disliked?" Maggie Haberman, a Times reporter and CNN analyst, asked on Twitter.

Late Monday night, Trump pivoted from the Times as a whole to one of the key sources for the story, ex-employee Barbara Res, who told The Times that Trump called her "Honey Bunch" and routinely commented on the physical appearance of women in the workplace.

Trump tweeted that he gave Res a top construction job "when that was unheard of, and now she is nasty. So much for a nice thank you!"

I gave a woman named Barbara Res a top N.Y. construction job, when that was unheard of, and now she is nasty. So much for a nice thank you! — Donald J. Trump (@realDonaldTrump) May 17, 2016

He added, "What Barbara Res does not say is that she would call my company endlessly, and for years, trying to come back. I said no."

Res was also interviewed by Megyn Kelly on Fox News on Monday. "Slowly but surely, he started saying more things that surprised me, up to this day," Res told Kelly.

Correction: An earlier version of this article said the Times' story ranks as its "most read story of the year," citing a tweet by a Times editor. The editor's information was incorrect.