Donald Trump was “incorrect”, Time magazine said, when he claimed on Saturday to have taken a “pass” on an interview and “major photo shoot” because the publication told him he was only “probably” going to be named its person of the year.

On Saturday morning, former Trump campaign manager Corey Lewandowski dutifully returned fire, co-opting the skirmish with the venerable magazine into the president’s continuing war with the press.

Lewandowski told Fox News: “The mainstream media has never wanted to give this president the credit that he’s deserved. I don’t know who else can be the Time magazine person of the year other than our president, Donald Trump.”

He added: “This president calls out the media when they’re dishonest, and that’s why the American people love him.”

Trump tweeted his thoughts on Friday evening, after a day of golf with Tiger Woods and world No 1 Dustin Johnson and, in his words, talking to Turkish president Recep Tayyip Erdoğan of Turkey about “bringing peace to the mess that I inherited in the Middle East”.

“Time Magazine called to say that I was PROBABLY going to be named “Man (Person) of the Year,” like last year,” Trump wrote, a little before 6pm ET, from Florida where he is spending the Thanksgiving break at his Mar-a-Lago club.

“But I would have to agree to an interview and a major photo shoot. I said probably is no good and took a pass. Thanks anyway!”

In the fashion of the times, just before 8.30pm ET, Time tweeted back: “The president is incorrect about how we choose Person of the Year. Time does not comment on our choice until publication, which is December 6.”

Time’s chief content officer, Alan Murray, put out a more strongly worded tweet, saying the president’s words were “amazing. Not a speck of truth here”.

Trump, 71, has a complicated relationship with Time. In June, the company asked Trump to remove a fake cover from display at his properties.

In January, in a controversial speech at CIA headquarters, he boasted that he had “the all-time record in the history of Time magazine” for appearances on (genuine) covers.

In March, in an interview with the magazine itself, he returned to the subject, saying: “I assume this is going to be a cover too, have I set the record? I guess, right? Covers, nobody’s had more covers.”

Trump has not had the most Time cover appearances. At the time of his Time interview he had 11, a long way behind Richard Nixon’s 55. According to Time’s own count, he has now appeared on its cover 14 times.

The magazine did name Trump its person of the year in 2016. He has thus been given the accolade as many times as the first winner, celebrity flier, Nazi sympathiser and fellow user of the “America first” slogan Charles Lindbergh (1927). Adolf Hitler (1938) also won the title once. Joseph Stalin (1939 and 1942) took it twice.

Trump’s predecessor Barack Obama (2008 and 2012) is among other two-time winners, as are former presidents George W Bush (2000, 2004), Bill Clinton (1992, 1998), Ronald Reagan (1980, 1983), Richard Nixon (1971, 1972), Lyndon Johnson (1964, 1967), Dwight Eisenhower (1944, 1959) and Harry Truman (1945, 1948).

Franklin D Roosevelt was given the honour three times, in 1932, 1934 and 1941. John F Kennedy was person of the year in 1961, Jimmy Carter in 1976 and George HW Bush in 1990.

Trump’s tweet on Saturday night duly produced a range of satirical responses on Twitter. The British tennis champion Andy Murray led the way, writing: “BBC just called to say I was PROBABLY going to be named sports personality of the year but I would have to agree to an interview and a major photo shoot. I said probably is no good and took a pass. Thanks anyway!”

Actor Julia Louis-Dreyfuss was among those who followed suit, tweeting that the New York Times “just called to say I was PROBABLY going to be named comedienne of the year but I would have to agree to an interview and a major photo shoot. I said probably is no good and took a pass. Thanks anyway!”