Press secretary Josh Earnest dismissed the president-elect’s unsubstantiated allegations that millions of people had cast illegal votes.
Trump also alleged voter fraud in Virginia, New Hampshire and California, states which Hillary Clinton won.
Earnest deferred to Trump’s team for further comment.
‘What I can say, as an objective fact, is that there has been no evidence produced to substantiate a claim like that,’ he told reporters at a White House briefing.
Trump, who won the all-important electoral college count, aired his grievances with the election result in a tweet on Sunday.
‘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,’ he wrote.
The president-elect’s Twitter outburst comes after the Clinton camp said it would support a vote recount in Wisconsin initiated by Green Party candidate Jill Stein.
Stein also notified the elections board in Michigan, where Trump’s 16 electoral votes were certified on Monday, that it would seek a statewide recount of the presidential election results.
Her campaign moved to do the same in Pennsylvania.
Trump won by two-tenths of a percentage point out of nearly 4.8 million votes, making it the closest presidential race in Michigan in more than 75 years.
He is the first Republican presidential nominee to win Michigan since 1988.
Stein’s recount effort was driven by the #recount2016 social media campaign, which has raised over $6.3m (£5m).
During her entire presidential run, Stein’s campaign only raised $3.5m.
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.
Clinton’s campaign’s general counsel, Marc Elias, said there was no evidence to conclude the election had been sabotaged.
But, he added, ‘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’.
Also on Monday, Trump met with former CIA director and retired army general David Petraeus, who was convicted of sharing classified information with his lover in 2012.
Petraeus is reportedly being considered for the role of secretary of state, the nation’s top diplomat.
Clinton was criticised by Trump during the campaign for her handling of classified information during her time as secretary of state.
Despite calling her handling of the classified information ‘extremely careless’, the FBI never found Clinton’s behaviour to be criminal.