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."
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.
Earlier on Sunday, the president-elect reminded his Democratic rival 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, Mrs Clinton 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".
The Green Party nominee reportedly wants to be sure computer hackers did not skew the poll in favour of Mr Trump.
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".