Before the elections, Trump had suggested that the results might be manipulated.
Neither he nor any of his aides has offered any evidence of the "millions" alleged to have voted illegally, nor did Trump explain why he would oppose a recount if illegal voting was such a serious problem, reported news agency AFP.
Trump's rival, Hillary Clinton, had won more popular votes. He further criticised the recount of votes in Wisconsin state, calling it a "waste of time".
Trump and his aides pushed back hard on Sunday as the calls for recount threaten the legitimacy of Trump's win.
In a series of tweets he quoted Clinton about the need to respect the electoral process, while continuing to wage an extraordinarily public battle over the makeup of his future cabinet, AFP said.
Very organized process taking place as I decide on Cabinet and many other positions. I am the only one who knows who the finalists are!
Trump's top aide Kellyanne Conway suggested on Sunday that the president-elect might rethink his decision of not pursuing Clinton's prosecution if her campaign pushes too hard for the recount.
Clinton's campaign has said it would join the process even though they have found no evidence of the results being manipulated in Trump's favour.
Green Party candidate Jill Stein, who received a fraction of the total vote in Wisconsin, filed for a recount of votes in the state. She further suggested a recount in the states of Michigan and Pennsylvania. Clinton's election lawyer, Marc Erik Elias, said they would also participate in recounts in Michigan and Pennsylvania if they are arranged.
Conway said on ABC that while Trump was being "magnanimous" toward Clinton, "I guess her attitude towards that is to have her counsel go and join this ridiculous recount," reported AFP.
Reince Priebus, Trump's chief of staff, said that while the president-elect is not "seeking methods and ways to persecute and prosecute Hillary Clinton", Trump would probably be "open to listening" should any new findings against her emerge from future investigations.
Some pundits caution that Trump's claim that millions of voters voted illegally should be taken as a warning sign of a potential future clamp down on voting rights under his administration.
The Trump voting tweet may be more than an ego spasm. It may also be a warning that voting is about to be made more difficult for millions