It follows reports Friday that Rosenstein floated the idea of secretly recording President Trump a year ago and that he raised the idea of using the 25th Amendment to remove Trump as unfit for office.
Other reports suggest that Rosenstein has resigned, or indeed, resigned before Trump had the chance to fire him.
Rosenstein strongly denied the allegations.
Trump is now in NY, where he will this week chair a meeting of the United Nations Security Council.
"Based on my personal dealings with the president, there is no basis to invoke the 25th Amendment", Rosenstein said.
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As of Sunday, Trump said he had not decided what to do about Rosenstein.
Further, The Washington Post quoted an unnamed individual saying Rosenstein quipped sarcastically after McCabe pushed for an investigation into the president, "What do you want to do Andy?" Rosenstein reportedly told close associates that he would one day be "vindicated" for being ordered to draft the memo justifying Comey's ouster.
But the latest move comes after a New York Times report of Rosenstein comments in 2017.
And it has been Rosenstein, in place of a reticent, camera-averse Mueller, who has conducted the major press briefings and made the visits to Capitol Hill since then.
The White House accepted his resignation, Bloomberg reported.
The deputy attorney general was overseeing the investigation of Russian election interference and links between the Donald Trump campaign and Moscow. He was reportedly angry that a memo he wrote about James Comey was cited as grounds for firing the Federal Bureau of Investigation director. If he's removed it could be the precursor to Trump maneuvering to put an end to the investigation. If Rosenstein were to leave office, U.S. Solicitor General Noel Francisco would be in line to oversee the Russian Federation probe.