Mr Biden said he was confident Mr Trump knew he was not going to win and had shown "incredible irresponsibility".
Mr Trump has launched lawsuits alleging unsubstantiated election fraud.
He has now also invited state lawmakers to the White House, hinting at a possible change in tactics.
Michigan's Republican lawmakers have been asked to meet him there on Friday.
All but one of Mr Trump's challenges has failed to make any real headway.
Mr Biden's victory margin in the public vote overall stands at more than 5.9 million. The victory in the US Electoral College system, which decides who becomes president, is projected to be 306 to 232.
Each state must certify its result over the next few weeks, although the deadlines vary. As the votes are certified, Mr Trump's chances of overturning the overall result will continue to dwindle.
Mr Trump would probably need to flip at least three states.
One possibility is that Mr Trump will try to get Republican-friendly state legislatures in key states to override the choice of voters and instead select electors favourable to the president.