Boris Johnson says that Vladimir Putin threatened to fire a missile at him. The Kremlin calls it ‘a lie.’

Britain’s former prime minister, Boris Johnson, has said that President Vladimir V. Putin of Russia made a veiled threat to fire a missile at him, a claim that the Kremlin on Monday dismissed as a lie.

Mr. Johnson recounted the exchange, which he said took place when he was prime minister in the run-up to Russia’s invasion of Ukraine last year, in an interview for a BBC documentary that was released on Monday. He said it came during a long phone call during which he had attempted to dissuade Mr. Putin from invading, arguing that doing so would lead to more sanctions and an increased NATO presence near Russia’s border.

“He threatened me at one point and said, you know: ‘Boris, I don’t want to hurt you but with a missile it would only take a minute,’ or something like that,” Mr. Johnson said of the Russian leader’s response. He added that Mr. Putin’s threat had been “jolly,” seeming to suggest that he had not taken it seriously.

“From the very relaxed tone that he was taking, the sort of air of detachment that he seemed to have, he was just playing along with my attempts to get him to negotiate,” Mr. Johnson said.

Full transcripts of phone calls between government leaders are not generally published, making it difficult to independently verify either side’s version of the conversation. The BBC said on its website that accounts of the call issued by the British and Russian governments at the time contained no reference to a personal threat by Mr. Putin.

The Kremlin was quick to reject Mr. Johnson’s recollection of the call.

“It’s a lie. There have been no missile threats,” the Kremlin’s spokesman, Dmitri S. Peskov, told reporters on Monday when asked about Mr. Johnson’s comments. Mr. Peskov said it was possible that the former British leader had not understood what Mr. Putin had been saying.

Mr. Johnson played a key role in rallying international support for Ukraine in the early weeks of the invasion and was one of the first Western leaders to visit the country after the war began in late February of last year.

Since announcing his resignation in July amid a series of scandals, Mr. Johnson has sought to portray his role in Ukraine, where he remains popular, as one of the most important achievements of his three years in power. His supporters frequently cite his advocacy for Ukraine as part of a case for Mr. Johnson’s potential return as party leader.

Earlier this month, Mr. Johnson paid another visit to Ukraine, an unusual move for a former leader, and held talks with President Volodymyr Zelensky, who called him a “true friend to Ukraine.”