"We will make a determination", Trump said.
He is now on his way to the White House.
On Monday morning, White House officials said Rosenstein had offered to resign to quell the controversy, while Justice Department officials said he had no intention of resigning but was heading to the White House with the expectation he would be fired.
Rosenstein was captured by photographers leaving the White House after his meetings Monday and was led out by Kelly.
Rosenstein is under fire for report he discussed secretly recording the president and enlisting Cabinet members to invoke the 25th Amendment to remove Trump from office; chief intelligence correspondent Catherine Herridge reports. His statements, however, did not deny that Rosenstein raised the prospect of using the 25th amendment or a wire to record the president.
Cummings has complained previously that Republicans controlling the oversight committee are not aggressively fulfilling their duty to investigate the Trump administration when warranted. But let me clear about this: "Based on my personal dealings with the president, there is no basis to invoke the 25th Amendment".
He added that there's nothing wrong with Trump wanting to speak with Rosenstein at the White House given the "volatility" of the situation. Rosenstein overseas Mueller's Russian Federation investigation.
Former FBI Deputy Director Andrew McCabe, whose private memos document comments made by Rosenstein, said Monday he he was concerned that a Rosenstein departure would put the investigation at risk. He received mixed messages.
Rumors of the impending firing of Deputy Attorney General Rod Rosenstein flooded the internet today - but the controversial figure has survived to see another day as the man responsible for overseeing the Mueller investigation.
Those developments came one week after Rosenstein laid the groundwork for the firing of Comey by writing a memo that criticized Comey's handling of the FBI investigation into Hillary Clinton's email server.