UPDATE 5-Trump says had 'great' meeting with Rosenstein; no plans to fire him

U.S. President Donald Trump said he had a "great" meeting on Monday with Deputy Attorney General Rod Rosenstein, the Justice Department official in charge of the federal investigation of Russian meddling in the 2016 presidential election, and has no plans to fire him.

There has been widespread speculation that Trump might oust Rosenstein, a frequent target of Trump's tweeted criticism, after a New York Times report that he had made remarks about Trump's fitness for office and offered to record conversations with him.

Rosenstein traveled with Trump on Air Force One to Orlando on Monday, where the president was to give a speech to police chiefs. Upon landing, Rosenstein was seen smiling and appeared at ease as he walked down the front stairs of Air Force One alongside Trump's chief of staff, John Kelly.

Trump and Rosenstein met for about 30 minutes during the flight, White House spokesman Hogan Gidley said.

Trump told reporters the meeting was "great." The White House declined to provide further details about the private discussion, but said Rosenstein still had a job.

Rosenstein has denied the Sept. 21 New York Times report as "inaccurate and factually incorrect." The article said that while Rosenstein had made the suggestions over concern about chaos in the administration, none of them actually came to fruition.

Asked earlier by a reporter if he had any plans to fire Rosenstein, Trump said, "No I don't, no."

Rosenstein oversees Special Counsel Robert Mueller's Russia investigation. Russia denies interfering and Trump says there was no collusion between his campaign and Moscow.

Firing Rosenstein before the Nov. 6 congressional elections could have political consequences. Democrats believe it would raise questions about whether Trump would shut down the Mueller probe, which could energize their voters in House and Senate races.

Trump told reporters earlier on Monday that he has a "good relationship" with Rosenstein.

"I didn't know Rod before, but I've gotten to know him, and I get along very well with him," he said. (Reporting by Roberta Rampton and Steve Holland; Additional reporting by Sarah N. Lynch and Doina Chiacu; Editing by Jonathan Oatis and Dan Grebler)