Moscow has denied USA intelligence agencies' conclusion that it interfered in last year's election campaign to try to tilt the vote in Trump's favour.
Also Wednesday, Senate Judiciary Chairman Charles Grassley said his panel will investigate the removal of former FBI Director James Comey and "any alleged improper partisan interference in law enforcement investigations".
Mr. Rosenstein took over the investigation into whether Russian Federation tried to tip the U.S election in favour of Mr. Trump after Attorney General Jeff Sessions recused himself in March.
It was unclear whether the president's comment confirming he was under investigation was based on direct knowledge or media reports that Mueller is examining whether the president obstructed justice by firing Comey.
The inquiries appear to be part of a fact-finding mission and it would ultimately be up to Mueller to decide whether there is enough evidence to recommend pursuing charges on any part of the investigation.
Deputy AG warns 'Americans should be skeptical about anonymous allegations'
Dianne Feinstein (D-CA), who said she's anxious that the President will try to fire both Mueller and Rosenstein . Rogers, the head of the National Security Agency; and Richard Ledgett, the former deputy director of the NSA .
At a Senate Intelligence Committee hearing last week, Coats and Rogers refused to say whether Trump asked them to intervene in the investigation, which is also examining whether the Trump campaign team colluded with Russian Federation during last year's presidential campaign.
The president has treated his attorney general to so much vitriol, Sessions reportedly offered to tender his resignation.
On Tuesday, he assured the Senate that he would refuse to follow an order to fire the special counsel, unless he believed it was given for good cause.
"I appointed him; I stand by that decision, " he said.
It was not immediately clear what prompted the release of that statement by Rosenstein, whether it was in response to recent stories that suggested the President was under investigation for obstruction of justice, or some other reason.
The criminal investigation of Trump puts his presidency in peril
The Post's report cited unnamed officials with knowledge of the ongoing Russian Federation investigation. Officially, Mueller spokesman Peter Carr told NPR's Carrie Johnson, "We'll decline to comment".
President Donald Trump speaks in the Roosevelt Room of the White House in Washington, Thursday, June 15, 2017, during an event on Apprenticeship and Workforce of Tomorrow initiatives.
Mueller's investigation appeared to be reaching a broadening circle of current and former officials.
"He is a man of extraordinary independence and integrity. and great character", Vice President Mike Pence told reporters on Wednesday, noting that the longtime Justice Department official "came to work, sat down and made his recommendation" to fire Comey.
The Post and The New York Times both reported that Mueller was seeking interviews with three Trump administration officials who weren't involved in Trump's campaign: Dan Coats, the director of national intelligence; Michael Rogers, the head of the National Security Agency; and Richard Ledgett, the former NSA deputy director. "Regulations way down, jobs and enthusiasm way up!"
White House aides have been instructed to not talk about Russian Federation investigation, but that doesn't apply to the President.
FBI Finds 'Hit List' On Body of Alexandria Shooter
Officer BaileyCapitol Police Officer David Bailey received a minor injury but was not shot, according to U.S. Matt Mika Mika, a lobbyist for Tyson Foods, was helping with practice when he was shot.
The order from 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. "I can go around them". It alleges that the FBI is violating the Freedom of Information Act (FOIA) because the Department of Justice has already ruled that the bureau should "expedite" CNN's FOIA request regarding the memos.
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