A source familiar with the Mueller investigation confirmed the report, saying an examination of possible obstruction of justice charges was "unavoidable" given testimony by former FBI Director James Comey, although the issue may not become the focus of the probe.
Trump had expressed the same outrage when Mueller, a former Federal Bureau of Investigation director from 2001 to 2013, was appointed last month by the US Department of Justice to probe Russian meddling.
Comey told a Senate panel last week he believed Trump fired him because of the Federal Bureau of Investigation's Russian Federation probe.
Meanwhile, Vice President Mike Pence has now hired legal counsel to represent him in the Russian Federation probe and there are media reports that the investigation has expanded to include the business dealings of White House adviser and Trump son-in-law Jared Kushner.
He had likened the appointment of the special counsel with the "single greatest witch hunt of a politician in American history".
The president complained the probe is unfair and wondered why his defeated Democratic opponent was not getting the same scrutiny. Several congressional committees are also investigating the Russian Federation matter.
Trump's tweet comes on the heels of a vague statement on the investigation from Rosenstein, released late on Thursday, and the spate of exclusive stories about the latest developments.
UK's May holds alliance talks with NIreland party chief
I can't negotiate with myself", he told European newspapers including the Financial Times. Foster's rivals in Northern Ireland, such as Sinn Fein's Gerry Adams, have objected.
Trump's digital volley appeared to be trained at Deputy Attorney General Rod Rosenstein, who recommended the firing last month of James Comey-an nearly unprecedented move that could yet imperil Trump's presidency. He said the president "sought my advice and input" on Comey's firing. Mueller is now leading the investigation into whether Russian Federation interfered in the 2016 presidential election and possible collusion with the Trump campaign.
Moscow has denied any interference. NPR's White House correspondent Tamara Keith reports. "Sad!" he wrote in one post.
Press Secretary Sean Spicer recently confirmed President Trump's tweets are in fact official statements.
Brand was sworn in as associate attorney general on May 22.
The memo to former transition team members on Thursday also seeks specific information on five people, the Times reported. The order also covers separate inquiries into several key Trump associates including former national security adviser Michael Flynn, campaign adviser Paul Manafort, foreign policy aide Carter Page and outside adviser Roger Stone.