"To preserve our constitution, our democracy, our basic integrity, he should be impeached," Biden told supporters at a rally in New Hampshire, adding his voice to that of other Democratic contenders.
"He's shooting holes in the constitution, and we cannot let him get away with it," added Biden.
Trump, however, showed no sign of buckling under pressure from the Democratic party probe into his alleged bid to damage Biden by strong-arming Ukraine to investigate the former vice-president.
Having threatened a constitutional crisis by refusing to cooperate with the congressional investigation, Trump predicted that the row would end up "being a big Supreme Court case".
He told reporters in the White House that his Republican party was being "treated very badly."
Democrats accuse Trump of stonewalling and obstruction.
"No one is above the law, not even President Trump," the Democratic majority leader in the House, Steny Hoyer, said on Wednesday. (AFP)