In subsequent tweets Trump said, "It would have been much easier for me to win the so-called popular vote than the Electoral College in that I would only campaign in 3 or 4 ... states instead of the 15 states that I visited. I would have won even more easily and convincingly (but smaller states are forgotten)!"
In one tweet, he named Virginia, New Hampshire and California as three states with "serious voter fraud."
California Secretary of State Alex Padilla denied Trump's claim about illegal voting in his state in a tweet Sunday night.
"It appears that Mr. Trump is troubled by the fact that a growing majority of Americans did not vote for him. His unsubstantiated allegations of voter fraud in California and elsewhere are absurd. His reckless tweets are inappropriate and unbecoming of a President-elect," Padilla tweeted.
The Trump transition team did not respond Sunday evening to a request for evidence to back up his claims.
Kay Stimson, a spokeswoman for the National Association of Secretaries of State, said it has "no information that can help to explain what sources or information are behind the basis of the tweets" by Trump.
The Clinton campaign's general counsel, Marc Elias, tweeted Sunday night, "We are getting attacked for participating in a recount that we didn't ask for by the man who won election but thinks there was massive fraud."
Elias announced Saturday in a post on Medium that the campaign would participate in the recount efforts but is not seeking to cast any doubt on the Electoral College results, adding that after looking into the matter, it did not find "any actionable evidence of hacking or outside attempts to alter the voting technology."
In a tweet storm Sunday morning, Trump attacked Green Party–backed efforts to recount the vote in the key states of Wisconsin, Michigan and Pennsylvania, where he narrowly defeated Clinton, calling the effort 'sad' and criticizing the Clinton campaign's participation in the effort.
"Hillary Clinton conceded the election when she called me just prior to the victory speech and after the results were in. Nothing will change," Trump tweeted.
A senior administration official told ABC News Saturday there did not appear to be any malicious activity related to the vote count and remained confident regarding the overall assessment of the election's integrity.
Stein has maintained her activities are in no way intended to benefit Clinton, whom she strongly criticized during the 2016 campaign.
George Martin, a former co-chairman of the Wisconsin Green Party who's involved in Stein's recount effort, said the party has been approached by computer scientists, election lawyers and other experts advocating vote recounts because of what they see as persuasive evidence of election result tampering. So far no verifiable proof of tampering or hacking has been revealed.
He said the recounts are not intended to change the outcome of the results but are a check on the process of counting votes.
ABC News' Alexander Mallin and Veronica Stracqualursi contributed to this report.