Under her leadership the Department of Justice “would have no choice” but to pursue criminal charges against Mr Trump due to revelations in Robert Mueller’s Russia report, the California senator said.
In an interview with NPR, Ms Harris - a former California attorney general - said she believed prosecutors "would have no choice and that they should [move against Mr Trump]. There has to be accountability.”
She added: “I do believe that we should believe Bob Mueller when he tells us essentially that the only reason an indictment was not returned is because of a memo in the Department of Justice that suggests you cannot indict a sitting president.
“But I’ve seen prosecution of cases on much less evidence."
Ms Harris, among the the leading candidates for the Democratic presidential nomination, was tipped to beat Mr Trump in the 2020 election by a new poll on Wednesday.
A string of Democrats, notably Joe Biden with a 13-point lead, polled better than the president, Quinnipiac University found.
Ms Harris' interview came as the House Intelligence Committee invited two former leaders of the FBI's national security branch to testify about the counterintelligence implications of Mr Mueller's investigation.
Mr Mueller did not find a criminal conspiracy between the campaign and Russia but did detail a series of interactions and outreach that have alarmed Democrats and accelerated calls from some in the party for impeachment proceedings and renewed investigations.
However, Nancy Pelosi, the top Democrat in the House, has repeatedly batted back calls to impeach Mr Trump. On Tuesday she said the scheme was "not even close" to having sufficient support.
Additional reporting by agencies