Judges have tossed out lawsuits in Michigan and Georgia, and experts say Trump's legal efforts have little chance of changing the election result.
Barr also told a Fox News TV host he was worried that an increase in mail-in voting could lead to a contested presidential election in November.
Tuesday will mark the first time that Barr has appeared before the House Judiciary Committee since taking the helm of the Justice Department in February of last year.
The standoff marks the latest in a series of unusual actions by Attorney General William Barr that critics say are meant to benefit Trump politically.
Trump's bid to militarize the US response to the protests has triggered a rare outpouring of condemnation from former US military officials, including Trump's first defense secretary, Jim Mattis.
Bowser said she had authorized the deployment of DC National Guard units as part of her response to the coronavirus pandemic, but did not request other military units.
William Barr is growing increasingly exasperated with the president commenting on ongoing Justice Department investigations on the social media platform.
More than 1,000 former department officials and legislators have now called for Barr to resign following Trump's twitter interference into the sentencing of Roger Stone.
Barr rejected the idea that President Donald Trump bore any of the blame for the national rise in antisemitism
Barr launched a review earlier this year to investigate Trump's complaints that his campaign was improperly targeted by U.S. intelligence and law enforcement agencies during the 2016 election.