Trump added that has a "good relationship" with Rosenstein and that there's been "no collusion".
"We had a very good talk, I will say".
"The press wants to know, 'What did you talk about?"' Trump said later to an audience of police officials.
Trump and Rosenstein had been scheduled to meet last week to discuss The New York Times report that flung Rosenstein into limbo.
As the plan was taking shape, Rosenstein went to the White House expecting he would be fired but wound up staying in his job.
Any termination or resignation of Rosenstein has the potential to affect the special counsel's investigation into possible co-ordination between Russian Federation and the Trump campaign since Rosenstein appointed former FBI director Robert Mueller to the job of special counsel and closely oversees his work.
Even before hearing, GOP plots aggressive Kavanaugh confirmation strategy
Gildo-Mazzon says she contacted Ford's lawyers after reading her account in a Washington Post story published on September 16. Ford's attorneys have said their client wants senators to ask the questions.
"It works, and it was meant for problems like Chicago", Trump said.
"No I don´t, no", Trump responded to a question from journalists at the White House about whether he plans to sack Rod Rosenstein.
Kelly was present for Monday's conversation between Rosenstein and Trump, the White House said, as was Rosenstein's top deputy at the Justice Department, Ed O'Callaghan.
Special counsel Robert Mueller's work been overseen by Rosenstein since Attorney General Jeff Sessions recused himself from the investigation.
Trump was also asked about musician Taylor Swift, who expressed her desire over the weekend to vote for Democrat Phil Bredesen over Rep. Marsha Blackburn, R-Tenn., in Tennessee's Senate race.
"Any effort to undermine the Mueller investigation will be obstruction of justice", Hoyer said.
Lawyer: FBI has completed Mark Judge interview
Opposition to Kavanaugh grew 4 percentage points after the hearing, apparently driven by people who previously were undecided. Trump initially was deferential to Ford, describing her late last week as a "very fine woman" and a "credible witness".
Critics predicted disaster, but Gotham's murder rate continued to fall even as cops cut back on stops - a point Hizzoner hammered home in a tweet after Trump spoke.
White House officials have told The Post that Trump is unlikely to fire Rosenstein before the midterm elections in November.
But even as Trump has made a decision to leave Rosenstein in place - for now - the matter of what Rosenstein said and proposed doing likely will remain a political issues heading into the homestretch of the midterms - and beyond.
It was not immediately clear whether Trump and Rosenstein talked about the controversy during their 45-minute-long conversation on the flight, where Kelly and another Department of Justice official, Ed O'Callaghan, were also present.
House Judiciary Chairman Robert W. Goodlatte says he plans to subpoena the Justice Department for memos Andrew McCabe wrote during his tenure as acting Federal Bureau of Investigation director.
Duchess Meghan Markle Throws a Ball with Guests at Coach Core Awards!
It was Megs' idea to incorporate the symbolism in a design which mirrored The Queen's Coronation gown in 1953. Doesn't get more romantic than that.