The US vice-president, Mike Pence, has denounced a New York Times article that suggested he is considering running for president in 2020 as “disgraceful and offensive”.

Pence said in a statement released on Sunday: “The allegations in this article are categorically false and represent just the latest attempt by the media to divide this administration.”

The article said some Republicans were moving to form a “shadow campaign” for 2020, as though the president, Donald Trump, were not involved. It said a number of Pence’s advisers had “already intimated to party donors that he would plan to run if Mr Trump did not”.

The story noted that the first-term Republican senators Tom Cotton of Arkansas and Ben Sasse of Nebraska had recently visited Iowa, a traditional trip for those sounding out runs for the White House. It also said the Ohio governor, John Kasich, a relative moderate who opposed Trump in the 2016 Republican presidential race, had visited the early voting state of New Hampshire.

The Times quoted a White House spokeswoman, Lindsay Walters, as offering a rejoinder: “The president is as strong as he’s ever been in Iowa, and every potentially ambitious Republican knows that.”

Trump is under growing pressure over legislative failures, particularly on healthcare changes, and investigations into links between his aides and family members and Russia. The special counsel Robert Mueller has summoned a grand jury in Washington, and Trump’s popularity rating remains historically low.

The president, who is beginning a 17-day stay at Bedminster, his New Jersey golf club that he insisted on Saturday was not a holiday, has touted the appointment of Neil Gorsuch to the supreme court, improving employment figures, stock market highs and progress against Islamic State in Iraq and Syria as proof of his success in the job.

“The American people know that I could not be more honoured to be working side by side with a president who is making America great again,” Pence said, before hitting a familiar note in White House criticism of the press.

“Whatever fake news may come our way, my entire team will continue to focus all our efforts to advance the president’s agenda and see him re-elected in 2020. Any suggestion otherwise is laughable and absurd.”

Kellyanne Conway, counsellor to the president, told ABC’s This Week on Sunday: “It is absolutely true the vice-president is getting ready for 2020 – for reelection as vice-president.”

The Times report, she said, was “complete fiction”. “Vice-president Pence is a very loyal, very dutiful, but also incredibly effective vice-president,” she added.

Pence, who is leading the president’s much-criticised commission into allegations of voter fraud, has remained relatively aloof from the turmoil affecting the White House. In February, Michael Flynn was forced to resign as national security adviser for misleading him over meetings with the then Russian ambassador.

The Democratic representative Maxine Waters, however, said this week: “When we finish with Trump we have to go and get” Pence.