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.
After Trump's tweet Friday morning, a person close to the president's legal team told NPR's Scott Horsley that the tweet referred to the Wednesday Washington Post report regarding possible obstruction of justice.
The website reported that Trump will sometimes interrupt conversations with associates to say, "I'm not under investigation".
The Twitter attacks came as Vice-President Mike Pence hired a personal lawyer to represent him in the intensifying investigation.
Trump's tweet comes less than a day after a unusual statement from a senior official in his administration. 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.
Russian Federation has repeatedly denied meddling in the 2016 United States presidential election, insisting that it does not meddle in the affairs of other countries. On Friday, the President tweeted he was under "investigation", which he called a "witch hunt" in another tweet. Rosenstein testified before the Senate Appropriations Committee on June 13.
"She added that she was "increasingly concerned" Mr Trump will fire both [investigative special counsel] Robert Mueller and Rosenstein". The transition, a nonprofit structurally separate from the Trump campaign, continues to operate with a small staff.
"Why is that Hillary Clintons family and Dems dealings with Russian Federation are not looked at, but my non-dealings are?" he asked. "Nice", Trump wrote in his first tweet. Comey was sacked by the president on May 9 while he was overseeing the investigation into potential Russian interference into last year's election and potential collusion with the Trump presidential campaign.
In an attempt to sound upbeat and to downplay the new developments in a controversy that has now reached the Oval Office, Trump also said that "despite the phony witch Hunt going on in America, the economic & jobs numbers are great".