President Trump has referred to Deputy Attorney General Rod Rosenstein, who appointed Robert Mueller as the special counsel for the Russia probe, as "a threat to his presidency," according to a report in The Washington Post.

The report, published Sunday, said Trump has referred to Rosenstein as "weak" and made fun of the deputy attorney general's testimony last week in front of the House Judiciary Committee.

The president has also complained about Rosenstein being "a Democrat," although the Justice Department official is actually a Republican, the Post said.

Rosenstein appointed Mueller the special counsel in May, after Trump fired FBI Director James Comey.

The report from the newspaper comes after a rumor swirled that Trump would fire the special counsel. But the president declared Sunday that he had no plans to do so.

Rosenstein last week testified that he sees no cause to fire Mueller, who has for months led the investigation into Russia's attempts to meddle in the 2016 U.S. presidential election and any potential ties between the Trump campaign and Moscow.

Mueller has secured guilty pleas from two Trump associates, including former national security adviser Michael Flynn. Mueller has also charged two other Trump campaign figures, including former Trump campaign chairman Paul Manafort.