A White House official on Friday told CNBC there were no talks about possibly firing Deputy Attorney General Rod Rosenstein.

"There are no discussions or consideration of firing Rod Rosenstein," the official said, speaking on the condition of anonymity.

Trump sparked concerns that Rosenstein's job would be at risk following Friday's release of a hotly debated Republican memo detailing alleged abuses in the FBI's probe into Russian meddling in the 2016 election.

Trump had offered an ominous response when a reporter asked whether he might fire Rosenstein and if, after reading the memo, he still has confidence in the deputy attorney general.

"You figure that out," the president said.

Rosenstein, a Trump appointee, assumed oversight of the Russia probe last year after Attorney General Jeff Sessions recused himself. Rosenstein then appointed Robert Mueller as special counsel in the investigation after Trump fired FBI Director James Comey in May.

Rosenstein and FBI Director Christopher Wray, whom Trump appointed to replace Comey, had urged the White House not to declassify the memo. Trump declassified the memo Friday.

Market watchers suggested that the uncertainty created by Trump's battle with the Justice Department loomed in the background as stocks sold off sharply on Friday.

"I think the fear of the memo is indirectly the fear of what's next to follow — that the deputy attorney general or head of the FBI might resign," said Art Cashin, UBS director of floor operations at the New York Stock Exchange. "That's not a one-day event. That recalls the Nixon 'Saturday night massacre,' even though those would be voluntary. It would start something that would last days or weeks."

A White House representative did not immediately respond to CNBC's request for comment about the stock market's performance Friday, including a nearly 666-point drop on the Dow Jones industrial average.

Trump often cites recent stock market gains as evidence that his economic policies are working.

— CNBC's Patti Domm contributed to this article.