This is a change from September 21, when Trump implied that he would fire Rosenstein after a New York Times report that claimed Rosenstein had said he would consider using the 25th Amendment to remove Trump from office.
Asked if Rosenstein still has the job, Gidley replied, "Yes". But Trump postponed the meeting amid an all-consuming confirmation process for Supreme Court Justice Brett M. Kavanaugh.
"No I don´t, no", Trump responded to a question from journalists at the White House about whether he plans to sack Rod Rosenstein.
Rosenstein has denied the September 21 New York Times report as "inaccurate and factually incorrect". Special Counsel Robert Mueller was appointed the next day.
Goodlatte also invited Rosenstein to meet with the committee privately.
"Marsha Blackburn is doing a very good job in Tennessee". The same day, Trump and Rosenstein spoke by phone while the president was at an United Nations conference in NY.
Trump said during his remarks that he has urged the city of Chicago to "strongly consider stop and frisk".
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Rosenstein had appeared close to being fired following U.S. media reports - which he denied - that he discussed secretly recording Trump and using the 25th constitutional amendment for removing presidents found to be unfit for office.
"Any effort to undermine the Mueller investigation will be obstruction of justice", Hoyer said.
Trump insisted several times during his 2016 campaign that Chicago should adopt it with gusto.
The Justice Department issued statements meant to deny the reporting, saying Rosenstein never pursued or authorized recording the president and did not believe there was a basis for invoking the 25th Amendment of the Constitution, which would involve the Cabinet and vice president agreeing to remove him.
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.
"Just look at what is now being exposed in the Department of Justice and the FBI", Trump had said at a rally, "look at what's going on".
Trying to appease conservative House Republicans who have threatened Rosenstein with impeachment proceedings, the deputy AG has agreed to talk to them in a private session.
"The press wants to know 'What did you talk about?' We had a very good talk, I will say".
Watch the clip above, courtesy of Fox News.