"I will be asking for a major investigation into VOTER FRAUD, including those registered to vote in two states, those who are illegal and even, those registered to vote who are dead," Trump said via Twitter.
White House spokesman Sean Spicer left open the possibility of the investigation in Tuesday's press briefing.
Trump has repeatedly asserted that he won the popular vote on November 8, once what he says are 3 to 5 million illegal votes are subtracted. His Democratic Party rival Hillary Clinton won the popular vote by 2.8 million.
Trump passed the 270-vote Electoral College threshold, which per US law is required to win the presidency.