We are suspending the campaign, the Maine Democrat announced in a video on social media.
Platner, an oyster farmer and Marine Corps veteran, won the primary in June despite already being surrounded by controversy. But after a woman came forward and accused him of rape, he has now chosen to step down, citing pressure from Democrats both in Maine and across the United States.
Liberal Maine has long been seen as the Democrats' best chance to win a seat in the Senate by unseating veteran Republican Senator Susan Collins in this fall's congressional elections.
Platner denies the rape allegations. Democrats must now find a replacement in Maine by July 27.
