Trump, who hired his own lawyer last month to represent him regarding probes by the special counsel and congressional committees, continued his harsh criticism of the investigations in series of tweets on Friday.
Rosenstein did not explain why he issued the statement.
Later, that position was contradicted by the President himself, in an interview with NBC's Lester Holt, when he stated that he had made up his mind to fire Comey before he had even seen the Rosenstein memo.
Sen. Richard Burr, R-N.C., right, chairman of the Senate Select Committee on Intelligence, and Vice Chairman Mark Warner, D-Va., left, listen as Attorney General Jeff Sessions testifies before the Senate Select Committee on Intelligence about his role in the firing of FBI Director James Comey and the investigation into contacts between Trump campaign associates and Russian Federation, on Capitol Hill in Washington, Tuesday, June 13, 2017.
Hours later, a source close to Trump's outside legal team said Trump did not intend his tweet to be confirmation of the investigation but rather was reacting to a Washington Post story on Wednesday about the probe.
The department would not comment on the record on whether Trump, who has repeatedly complained about leaks on the case, requested the statement.
Deputy Attorney General Rod Rosenstein submitted a widely circulated memo to the president last month raising concerns over Comey's performance, but Trump later asserted that he had already made the decision himself to fire Comey.
Trump has told associates he has the legal authority to fire Mueller.
On the following day in an Oval Office meeting with Russian officials, the President described his FBI chief as a "nut job" and "crazy" and expressed relief that the "pressure " of the Russia investigation had been lifted by the firing of Comey.
Farmers protest: Shivraj Singh Chouhan continues fast for 2nd day
He also announced that the agricultural land would be acquired only after the consent of the farmer. First, the government said that the police didn't fire at farmers during the agitation.
Several White House officials and Trump associates insisted on anonymity in order to discuss the president's views of the unfolding investigation.
After Attorney General Jeff Sessions recused himself from the probe, Deputy Attorney General Rod Rosenstein became the person in charge.
The order by the general counsel for the transition team casts a wide net on documents that could shed light on ties between Trump's presidential campaign and representatives of Russia's government.
Trump's tweets came after the top lawyer for his transition team warned the organization's officials to preserve all records and other materials related to the Russian Federation probe.
The memo to former transition team members on Thursday also seeks specific information on five people, the Times reported, They include Paul Manafort, Trump's former campaign manager; Rick Gates, Manafort's business partner; Carter Page, a former foreign policy adviser; former national security adviser Michael Flynn; and Roger J. Stone Jr., an informal adviser to Mr. Trump.
"He brought that recommendation to the President" and Trump agreed, Pence concluded.
During an appearance in Florida on Friday, Vice President Mike Pence said his hiring of his own lawyer to help him in the Russian Federation inquiry was a "very routine" move.
His time under Bush, Obama and then Trump made him the longest-serving US attorney in the nation's history when he was confirmed to his current role under Sessions.
Flynn, who was forced out in February, is a subject in investigations by intelligence committees in the House and Senate, as well as the Federal Bureau of Investigation. A former prosecutor, Dowd may be best known to the public for leading investigations on behalf of Major League Baseball, including a probe of allegations of improper gambling by baseball player Pete Rose that preceded Rose's lifetime ban.