US President-elect Donald Trump has asserted he won the popular vote on 8 November "if you deduct the millions of people who voted illegally".
The Republican, who won the all-important electoral college count, offered no evidence to back his claim.
It comes after the camp of Democratic rival Hillary Clinton said it would support a vote recount in Wisconsin initiated by a Green Party candidate.
Mrs Clinton won about two million votes more than Mr Trump in the popular vote.
However, Mr Trump surpassed the required 270 electoral votes to win the presidency. This was based on the state-by-state contests.
In a tweet, he wrote: "In addition to winning the Electoral College in a landslide, I won the popular vote if you deduct the millions of people who voted illegally."
No evidence for Trump claim, says BBC's Anthony Zurcher
It's a classic Donald Trump move. Take an accusation, and turn it on an accuser. His opponents want a recount in states he won? Then he'll allege massive voter fraud in states carried by Hillary Clinton.
There is, of course, no evidence of the "millions" of illegal votes that Mr Trump says were cast for Democrats. If there were, it would merit a full investigation and not a series of Sunday-morning tweets from the president-elect. The veracity of these accusations seems of little import to Mr Trump.
What matters is that by going on the offensive, he turns a story about the legitimacy of his narrow wins in key states into a muddled mess. As he has done in the past, he raises the volume in hopes of drowning out a negative story.
The irony is that, in this case, it seems a pointless undertaking. The Green Party-funded recounts will almost certainly fail to reveal electoral malfeasance. Mr Trump could have let them proceed without comment and avoided any controversy.
Then again, for this president-elect, controversy is like water to a fish. It surrounds and sustains him. Perhaps he can't function without it.
In his follow-up tweets, the Republican wrote: "It would have been much easier for me to win the so-called popular vote than in 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)!"
Mr Trump also alleged "serious voter fraud" in Virginia, New Hampshire and California - states won by Mrs Clinton - accusing US media of not reporting on that issue.
The president-elect's tweets came as his transition team faced infighting over Mitt Romney's candidacy for secretary of state.
In TV appearances on Sunday, senior adviser Kellyanne Conway spoke out against Mr Romney's potential appointment, saying Mr Trump's supporters felt "betrayed" he would consider the former governor for the prominent role.
She said Mr Romney, who was one of Mr Trump's fiercest critics during the campaign, "went so far out of his way to hurt" the president-elect.
Is there any evidence of illegal votes?
- Unsubstantiated claim was started by self-styled conservative voter fraud specialist Greg Phillips who tweeted "Number of non-citizen votes exceeds 3 million"
- Mr Phillips declined to release any evidence
- His tweets were picked up by right-wing websites like Infowars.com, which has made false claims in the past
- Fact-checking website Snopes.com says there is "zero evidence" that "illegal aliens" voted in election
Mr Trump, meanwhile, reminded Mrs Clinton on Sunday that she had already admitted defeat, and published remarks from the presidential debates in which she had urged an acceptance of the poll results.
At the time, his Democratic rival was reacting to Mr Trump's refusal to respect the outcome.
Mr Trump narrowly beat the Democratic candidate in Wisconsin, where a recount of the votes was initiated last week by Green Party candidate Jill Stein.
Dr Stein also wants recounts in Michigan and Pennsylvania, citing "statistical anomalies".
Concerns over possible Russian interference had been expressed in the run-up to the vote.
The US government has said Russian state actors were behind hacks on the Democratic National Committee, a claim denied by Moscow.
Results would need to be overturned in Wisconsin, Michigan and Pennsylvania to alter the outcome of the November presidential election - something analysts say is highly unlikely.
Mrs Clinton's campaign has said it will participate in Wisconsin's recount.
Her campaign's general counsel, Marc Elias, said there was no evidence to conclude the election had been sabotaged, but "we have an obligation to the more than 64 million Americans who cast ballots for Hillary Clinton to participate in ongoing proceedings to ensure that an accurate vote count will be reported".