"I hereby demand, and will do so officially tomorrow, that the Department of Justice look into whether or not the FBI/DOJ infiltrated or surveilled the Trump Campaign for Political Purposes - and if any such demands or requests were made by people within the Obama Administration!" the president tweeted Sunday.
Mueller is mandated to investigate the alleged Russian interference in the 2016 USA presidential election and any potential collusion between the Trump campaign and Moscow, among other matters that may arise from the investigation.
Trump met with FBI Chief Christopher Wray and Deputy AG Rod Rosenstein about congressional demand for documents related to an FBI informant's meetings with Trump presidential campaign advisers.
"You do a great disservice to our Nation & the Republican Party if you continue to enable Mr. Trump's self-serving actions", he told House Speaker Paul Ryan (R-Wis.) and Senate Minority Leader Mitch McConnell (R-Ky.).
Mr Trump's latest demand came amid a series of tweets on Sunday denouncing a "witch hunt" that, he said, had found no collusion by his campaign with Russian Federation.
The department of justice inspector general will examine the informant's role as part of its ongoing review of the FBI's requests to a secretive court - under the Foreign Intelligence Surveillance Act - for permission to wiretap Page during the initial stages of investigation of Russian meddling.
Jeff Sessions, the United States attorney general, and Mr Rosenstein, his deputy, have both been figures of Mr Trump's public anger in the past.
China Says It Can't Guarantee No More Trade Tension With US
While about a third of USA production goes to the Asian country annually, China a year ago bought more of the oilseed from Brazil. Analysts said the talks may have helped to ease tensions at least slightly between the world's two biggest economic powers.
President Donald Trump has asked the US Department of Justice to investigate whether the Federal Bureau of Investigation spied on his 2016 election campaign for "inappropriate purposes" on the orders of people in the Obama administration.
The inspector general will expand his probe into the handling of investigations during 2016 election season to include any "irregularities" involving FBI or Justice Department "tactics" - language vague enough to be essentially meaningless.
It was possible that Rosenstein punted the matter to the inspector general to avoid a direct face-off between the White House and the Justice Department.
"His "demand" DOJ investigate something they know to be untrue is an abuse of power, and an effort to distract from his growing legal problems", Schiff added.
The question now is whether Trump's own Justice Department officials have the courage to buck him.
There was speculation from USA media commentators that Mr Trump's demand was an attempt to force senior justice officials into resigning. But intelligence officials say turning over the documents would put the source at risk, according to The Washington Post.
Trump had harbored suspicion since previous year that his campaign had been spied by the Obama administration.
On Sunday, legal experts wondered how the Trump-appointed heads of the FBI and DOJ would respond to his demand for an investigation into the probe looking at his campaign if the Justice Department's accommodation ends up not being enough. She said the officials will "review highly classified and other information they have requested", but did not provide additional detail.