President Donald Trump last summer wanted to fire special counsel Robert Mueller, who is leading an investigation into Russian interference in the 2016 election, but backed off when his top White House lawyer said he would resign rather than carry out the order, a person familiar with the matter said.

The president, who is in Davos, Switzerland, for an economic conference, denied on Friday that he considered dismissing Mr. Mueller.

“Fake news. Fake news,” Mr. Trump said as he arrived in the World Economic Forum on Friday morning for meetings with foreign leaders ahead of his address this afternoon.

The New York Times first reported that Mr. Trump had ordered the firing.

The Wall Street Journal has reported that West Wing officials expressed concern that White House counsel Don McGahn would quit out of frustration over the lack of protocols surrounding meetings between Mr. Trump and Jared Kushner, his son-in-law, whose activities are under scrutiny in the Russia probe. This happened around the same time last summer as Mr. Trump wanted to fire Mr. Mueller, the person familiar with the matter said.