In remarks at the International Association of Chiefs of Police Annual Convention in Orlando, President Trump announced that he has directed the attorney general's office take a more active role in curbing Chicago's wave of gun violence, and said he has recommended the Justice Department work with local authorities to implement "stop and frisk" in the city.
Trump - who had delayed a previously announced White House meeting in which expectations were high that Rosenstein would depart - said they were going to talk Monday during a trip to Florida.
The White House said conversations between Rosenstein and Trump would continue after Trump returned from UN General Assembly events.
The deputy attorney general appointed former FBI Director Robert Mueller to his special counsel post and closely oversees his work.
Rosenstein, who oversees special counsel Robert Mueller's Russian Federation probe, denied the reports.
Trump said earlier in the day that he had "a very good relationship" with Rosenstein and was eager to speak with him aboard Air Force One on the flight to Florida. But we had a very good talk, I will say. They did talk, for about 45 minutes, but not alone, a White House spokesman said.
Rosenstein denied a September 21 report in the New York Times that alleged he wanted to surreptitiously record Trump and discussed rallying cabinet members to invoke the 25th amendment to remove the president from office. "It works and it was meant for problems like Chicago".
Trump's visit to the City Beautiful came days after a U.S. Senate Committee voted to confirm Judge Brett Kavanaugh to the U.S. Supreme Court. Advisers had also cautioned Trump against doing anything dramatic in the weeks before the midterm elections next month, suggesting Rosenstein's job is safe at least for now.
He did not disclose details of their conversation, but referred back to the president's comments as he left the White House saying he did not intend to fire Rosenstein.
As a candidate, Trump even went as far as advocating a nationwide "stop-and-frisk" policy for law enforcement, but after heavy criticism clarified that he was just specifically referring to Chicago.
Democrats and some Republican lawmakers have warned Trump for months about firing either Rosenstein or Attorney General Jeff Sessions.
But even as Trump has chose 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.
Rosenstein's job security has been under question since news reports last month that he had discussed possibly secretly recording Trump to expose chaos in the White House and invoking constitutional provisions to get him removed from office.