The tweet came around 9:10 a.m. Friday.
Moscow has denied U.S. intelligence agencies' conclusion that it interfered in last year's election campaign to try to tilt the vote in Trump's favour.
Earlier this week, the investigation led by special counsel Robert Mueller appeared to move closer to Trump.
Just 22 percent of Americans support Trump's decision to fire former FBI Director James Comey, compared with the more than half of Americans who disapprove of the president's decision.
"The Vice-President is focused entirely on his duties and promoting the President's agenda and looks forward to a swift conclusion of this matter", a Pence spokesman said.
That will only add to a sense of foreboding that pervades the White House, from the crammed collective workspaces of junior officials all the way to the Oval Office.
He dismissed as phoney the idea his campaign colluded with any Russian effort to sway the 2016 election. "Witch Hunt", the president wrote on Twitter. Thanks to his firing of Comey and Comey's personal memos that accuse #45 of trying to get him to drop the investigation against ex-national security adviser Michael Flynn, the President is reportedly now under investigation for obstruction of justice. While the investigation had originally been focused on potential collusion between the Trump campaign and Russian Federation, the Post reported, the obstruction inquiry began after Trump fired Comey. He is reportedly interviewing three top intelligence officials - Director of National Intelligence Dan Coats, National Security Agency Director Mike Rogers and retired deputy NSA director Richard Ledgett - as part of the probe as early as this week.
The obstruction of justice investigation into Trump began days after Comey was sacked, according to people familiar with the matter, the Washington Post said. Mr. Trump later contradicted his own staff, saying on May 11 he had the Russian Federation issue in mind when he fired Mr. Comey. A spokesman for him declined to comment on Wednesday.
As the legal rope has tightened, Trump's allies have gone on the offensive, questioning Mueller's credibility and floating the idea he may be fired.
The second, the source continued, is whether if any potential offences were committed, Trump or others attempted to cover them up or obstruct the investigation into them.
Mueller, a former director of the Federal Bureau of Investigation, is leading the Russian probe after being appointed by the Deputy Attorney General Rod Rosenstein in the Department of Justice.
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.