WASHINGTON — President Trump again insisted on Saturday that he was not under investigation by Robert S. Mueller III, the special counsel investigating Russian influence on the 2016 election, adding that “there’s been no collusion, there’s been no crime.”

“Everything I’ve done is 100 percent proper,” Mr. Trump said during a news conference at Camp David, where he was asked about a New York Times report that he had pressed Attorney General Jeff Sessions not to recuse himself from the Russia inquiry. “That is what I do, is I do things proper.”

The president said the Times article, which reported that Mr. Trump had sought to protect himself by keeping Mr. Sessions in charge of the investigation, was “off,” though he did not elaborate.

The two primary issues that Mr. Mueller appears to be investigating are whether Mr. Trump obstructed justice while in office and whether there was collusion between the Trump campaign and Russia.