Upon landing in Orlando, Florida, Trump told reporters that his 30-minute conversation with Rosenstein had been "great".
That means Rosenstein is still overseeing the Justice Department's Russian Federation election meddling probe that has so riled Trump.
The International Association of Chiefs of Police is the world's largest professional association for police leaders. "We'll be talking on the plane", Trump said.
"The press wants to know, 'What did you talk about?'" Trump said at the start of his speech after he thanked Rosenstein for being there and noted the intense media interest.
The documents reportedly chronicle conversations in which Rosenstein discussed the idea of secretly recording Trump for the objective of invoking the 25th Amendment to remove him from office.
"I didn't know Rod before, but I've gotten to know him", Trump said at the White House.
Rosenstein assumed supervision of the investigation after Attorney General Jeff Sessions recused himself
President Donald Trump touted his commitment to law enforcement in Orlando today, urging Chicago to adopt controversial "stop-and-frisk" policies and calling the critics and accusers of newly appointed U.S. Supreme Court Justice Brett Kavanaugh "evil people".
Fresh off his victory of Judge Brett Kavanaugh's confirmation to the Supreme Court, President Trump doubled-down on his commitment to being the "law and order" president by suggesting Chicago could curtail gun violence by using "stop and frisk" - the famous NY law enabling officers to temporarily detain, question, and frisk civilians upon "reasonable suspicion". He met in person with White House chief of staff John Kelly and spoke by phone with Trump during a tumultuous day that ended with him still in his job.
Trump had previously indicated he would prefer to keep Rosenstein in his post, but offered no definitive indication of Rosenstein's fate until his comments on Monday morning. "There's no reason for what's going on there", Trump said, adding that Chicago should "strongly consider stop and frisk". 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.
Both men will likely see their futures re-evaluated after the elections, Trump advisers have said.
Rosenstein had appeared close to being fired following United States 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.
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