Aides to President Joe Biden like to say he is transparent with the reporters who cover him.

This might not have been what they meant.

In a hot-mic moment that may enter the annals of presidential insults, Biden directed an under-the-breath expletive on Monday towards Peter Doocy, the White House correspondent for Fox News, that was amplified by a live microphone onto television and laptop screens around the world.

The exchange came as reporters were being ushered away from a brief appearance by Biden in the East Room. Doocy called out a question: “Do you think inflation is a political liability in the midterms?”

Biden’s patience was low. And the volume was up.

“It’s a great asset,” the President said in a sarcastic tone, seemingly to himself. “More inflation. What a stupid son of a b****.”

Doocy is a reliable needler of Biden, although the President often appears more amused than angered by their jousts. Their sometimes spiky exchanges have become a regular feature of Biden’s public appearances.

On Monday night, Doocy said on Fox News that the President called his cellphone about an hour after the incident and, in his words, “cleared the air”.

Peter Doocy.

“He said, ‘It’s nothing personal, pal’,” Doocy told the host Sean Hannity. “We were talking about just, kind of, moving forward. And I made sure to tell him that I’m always going to try to ask something different than what everybody else is asking, and he said, ‘You got to’.”

When Hannity pressed on whether Biden had apologised, Doocy laughed and demurred. “Sean, the world is on the brink of, like, World War III right now with all this stuff going on,” he said. “I appreciate that the President took a couple minutes out this evening while he was still at the desk to give me a call and clear the air.”

It was hardly the first time that harsh language intruded on the typically PG-rated interactions between powerful politicians and reporters.

George W. Bush, while running for President in 2000, was caught on a live microphone using an epithet to refer to a New York Times reporter. (His running mate, Dick Cheney, was overheard affirming Bush’s observation: “Big time.”)

No accident was required for Americans to hear the insults lobbed by former President Donald J. Trump at his interlocutors in the media. Trump deemed Jim Acosta of CNN “a rude, terrible person”, called Jonathan Karl of ABC “a disgrace”, and said April Ryan, now of TheGrio, was a “loser”, to name but three examples. Among other moments, Trump once mocked the physical disabilities of a Times reporter to entertain his supporters at a campaign rally.

On Monday, speaking afterwards on Fox News, Doocy recounted what happened with a lopsided grin. “I couldn’t even hear him because people were shouting at us to get out,” he said.

Dana Perino, a Fox News host who served as White House press secretary under Bush, told Doocy that he should embrace the moment. “You might even have a book title,” she joked.

New York Times News Service