A longtime friend of President Trump said on Monday that Mr. Trump was considering whether to fire Robert S. Mueller III, the special counsel investigating possible ties between the president’s campaign and Russian officials.

The startling assertion comes as some of Mr. Trump’s conservative allies, who initially praised Mr. Mueller’s selection as special counsel, have begun trying to attack his credibility.

The friend, Christopher Ruddy, the chief executive of Newsmax Media, who was at the White House on Monday, said on PBS’s “NewsHour” that Mr. Trump was “considering, perhaps, terminating the special counsel.”