Meanwhile, Capitol Hill Democrats are focusing on a line in the attorney general's summary that says Mr Mueller's report "does not exonerate" Mr Trump of obstruction of justice, even though Mr Barr concluded on Sunday there was insufficient evidence that Mr Trump had committed a crime.
The Republican president and his allies in Congress went on the offensive a day after the release of a summary of Mueller's report gave him a political victory ahead of his 2020 re-election bid, with no allegations of criminal wrongdoing brought against him at the end of a almost two-year-long inquiry.
Democrats are calling on Barr to testify about how he reached his conclusion on the question of potential obstruction of justice by the president, and they have called for the public release of the full Mueller report.
He even accused those responsible for launching it of "treasonous things against our country" and said they "certainly will be looked into".
The top Democrat on the Judiciary Committee, Senator Dianne Feinstein, said Graham had the prerogative as chairman to bring whatever he wants before the committee.
Those investigations could now shift to issues involving emoluments and potential conflicts of interest posed by Trump's business empire, especially as Trump and close allies still face federal investigations in NY.
Given the report, Democrats seemed more likely to focus on their ongoing investigations, calls for transparency and frustrations with Barr, rather than engaging with the talk of impeachment that has been amplified on Pelosi's left flank. He added, "I've been looking at them for a long time".
Speaking in the Oval Office, he said no other president should have to be investigated over "a false narrative".
Much of the charges against the Trump associates related to lying to Congress or federal investigators and none of them directly related to the question of collusion between his campaign and Russian Federation. They lied to Congress.
Trump spent months railing against former Justice Department officials, including former FBI Director James Comey, accusing them of an illegal witch hunt for the goal of delegitimizing his presidency.
In an appearance on NBC's "Today" programme, Sanders said: "The media and Democrats have called the president an agent of a foreign government. I say it very strongly".
From the first turbulent moments of Donald Trump's presidency some Democrats have found solace in thinking that he might be impeached, the highest rebuke that Congress can deliver to an American president.
Barr signaled in his letter that more information of the Mueller report may be released in the future. He has also falsely claimed that the investigation was based on memos compiled by former British spy Christopher Steele, and even blamed former senator John McCain, who died previous year, for passing the memos to the FBI. "This case is closed", said House Republican Leader Kevin McCarthy in a statement. It was a false narrative. He said on Monday that "we can never let this happen to another president again".
Qatar Airways CEO has confidence in Boeing airplanes
After the update, the system will rely on data from more than one sensor before it automatically pushes the plane's nose lower. Boeing has not said what it expects to pay to relatives of the people who died in the Lion Air and Ethiopian Airlines crashes.
Trump had repeatedly accused Mueller, a former Federal Bureau of Investigation director, of running a "witch hunt" with a team of "thugs" and having conflicts of interest. He said he will be consulting with Mueller to determine what else can be released.
Trump also said he had not thought about pardoning anyone convicted or who pleaded guilty in the Mueller probe.
They reportedly include Mr Trump's company, the Trump Organisation, as well as the committee that put on the 2017 presidential inauguration.
While Democrats have said Mr Barr's letter should not be considered the final word on what Mr Mueller found, the president still claimed total vindication. His stance, based on less than 48 hours' review of Mueller's report, felt like a non sequitur, since under current Justice Department guidelines presidents can't be criminally indicted anyway.
The statement also said Congress needs "the full report and the underlying documents so that the Committees can proceed with their independent work, including oversight and legislating to address any issues the Mueller report may raise". The House of Representatives earlier in March voted 420-0 in favour of making the report public.
By Barr's account, Mueller did not implicate or exonerate Trump of obstruction of justice, effectively punting that question.
Donald Trump claims he has been completely exonerated by an inquiry into allegations Russian Federation conspired to help him win the 2016 election.
But investigators can't give a definitive answer on whether the president obstructed justice or not.
A person familiar with the matter said there were no plans at this time to show the Mueller report to the White House.
Handler tweeted: 'I will admit my feelings for Mueller are conflicted now and my sexual attraction to him is in peril, but I still believe there is a lot more to come, and we must all march in the streets if we don't see that report'.
The Kremlin said on Monday that President Vladimir Putin was ready to improve ties with the United States following the release of Barr's summary and called on Washington to formally recognise there was no collusion. Now he can focus on finding, disabling and punishing those who worked for Russian Federation to attack the United States election.
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