WASHINGTON — Just before Election Day, when The Wall Street Journal uncovered a secret deal by the National Enquirer to buy the silence of a former Playboy model who said she had an affair with Donald Trump, his campaign issued a flat denial.

“We have no knowledge of any of this,’’ Trump’s spokeswoman, Hope Hicks, told the newspaper. She said the claim of an affair was “totally untrue.’’

Then last week, when The New York Times revealed the existence of a recorded conversation about the very payment Trump denied knowing about, Trump’s lawyer, Rudy Giuliani, described the recording as “exculpatory’’ — suggesting it would actually help Trump if it became public.

Finally, the tape has become public. And it revealed the statements by Hicks and Giuliani to be false. The recording, which was broadcast by CNN late Tuesday, shows Trump directly involved in talks about whether to pay the Enquirer for the rights to the woman’s story.

The recording, and the repeated statements it contradicts, is a stark example of how Trump and his aides have used falsehoods as a shield against tough questions and unflattering stories. Building upon his repeated cry of “fake news,’’ he told supporters this week not to believe the news. “What you’re seeing and what you’re reading is not what’s happening,’’ the president added.

In a capital where politicians have made an art form of the nondenial denial, press secretaries typically reserve their on-the-record denials for stories that are outright false. Candidates can weather most embarrassing stories and press officers know that getting caught in a lie makes things worse.

But Trump has turned that thinking on its head. When faced with the evidence of its misstatements, the administration sidesteps and moves on. “I’m not going to get into a back-and-forth,’’ the White House press secretary, Sarah Huckabee Sanders, said last month when confronted with her unequivocal, and false, denials that Trump had dictated his son’s misleading statement about meeting with Russians.

The tape that surfaced Tuesday concerned the former model, Karen McDougal, who says she began a nearly yearlong affair with Trump in 2006. Shortly before the 2016 election, she sold her story for $150,000 to The National Enquirer. But the tabloid, which was supportive of Trump, sat on the story, a practice known as catch and kill. It effectively silenced McDougal for the remainder of the campaign.

The legal implications of the taped conversation for Trump are unclear. Federal prosecutors in Manhattan are investigating whether Trump’s longtime personal lawyer, Michael D. Cohen, committed bank fraud or violated campaign finance laws by arranging payments to silence women critical of Trump.

The recording is potentially significant because it places McDougal in the context of the presidential campaign. Trump and Cohen talk polling, surrogates, fending off journalists, and embarrassing deals. But it is not clear whether that creates legal problems for Trump.

The recording was among 12 handed over to prosecutors from a trove of Cohen’s material that FBI agents seized in April. It is the only recording of substance between Cohen and Trump, according to people familiar with the material. Others include Cohen speaking to broadcast media figures, according to the people.

In the recording, Trump does not appear surprised to hear about the arrangement with the Enquirer’s parent company, American Media Inc. Cohen describes the agreement with “our friend David,’’ a reference to the company’s chief executive, David Pecker.

The tape surfaced as part of a widening rift between Trump and Cohen, his once-trusted adviser. Cohen has all but advertised his willingness to cooperate with federal prosecutors, an arrangement that could unearth many of the secrets that he helped bury in a decade of work as Trump’s fixer. No such cooperation deal has been reached, and prosecutors typically do not make such arrangements until they have finished reviewing the evidence they have collected.

The tape also shows how enmeshed the Trump Organization had become in politics and the effort to protect Trump’s image. Cohen can be heard telling Trump that he had consulted with the company’s chief financial officer, Allen Weisselberg, “when it comes time for the financing’’ of the payments to the Enquirer’s parent company.

“Wait a sec, what financing?’’ Trump is heard saying.

“Well, I’ll have to pay him something,’’ Cohen then says.

Weisselberg was also involved in structuring Cohen’s reimbursements of more than $400,000 after he parted ways with the Trump Organization. Those reimbursements to Cohen are said to have included money he spent to silence an adult-film actress named Stephanie Clifford, who goes by the stage name Stormy Daniels. She also alleged a previous affair with Trump he has denied.

When the recording surfaced, Trump’s lawyers drafted a transcript and circulated it to reporters. In their version, Trump told Cohen “don’t pay with cash’’ and then says, “check.’’

Cohen’s lawyers argued that Trump’s team manufactured a dialogue to make it more favorable for their client. “They have been getting away with saying that a lie is the truth and don’t believe the media,’’ said Lanny J. Davis, a lawyer for Cohen. “But they walked into a trap here because a tape is a tape. It’s a fact. If you’re for Donald Trump, don’t believe me. I’m a Democrat. Believe your own ears.’’