Legal challenges to recount efforts taking place in a number of US states have been filed.
Green Party candidate Jill Stein has called for recounts in Wisconsin, Michigan and Pennsylvania - all states were Mr Trump achieved narrow victories of less than 1% over Hillary Clinton.
Ms Stein has raised almost $7 million through crowdfunding to support the effort. The recount process has already gotten underway in Wisconsin.
In a series of Tweets, Michigan Attorney General Bill Schuette wrote:
Today I am filing suit to stop @DrJillStein's frivolous, expensive recount request.
— A.G. Bill Schuette (@SchuetteOnDuty) December 2, 2016
"[Michigan] voters rejected Dr Jill Stein's candidacy and her refusal to accept verified results poses an expensive & a risky threat to [Michigan] taxpayers," he explained.
"It is inexcusable for Stein to put MI votes at risk of paying millions and potentially losing their voice in the [Electoral] College. I have filed an emergency motion with the Mich Supreme Court to bypass the Court of Appeals to ensure a timely process," he added.
The New York Times reports a lawsuit has been filed against the Wisconsin Elections Commission, and suggests that Mr Trump and his allies are also attempting to halt legal proceedings by Jill Stein in Pennsylvania.
According to The Guardian, attorneys in Pennsylvania for the President-elect have accused Jill Stein of “bringing mayhem” to the election process.
Marc Elias, counsel for the Clinton campaign, last week indicated that the campaign will participate in the recount - although stressed they themselves had not uncovered any actionable evidence.
"We [participate] fully aware that the number of votes separating Donald Trump and Hillary Clinton in the closest of these states”Š -”Š Michigan”Š - well exceeds the largest margin ever overcome in a recount," he wrote in a Medium post.
"But regardless of the potential to change the outcome in any of the states, we feel it is important, on principle, to ensure our campaign is legally represented in any court proceedings and represented on the ground in order to monitor the recount process itself," he added.
President-elect Trump has posted several tweets criticising the recount effort, although has also claimed - without evidence - that 'millions of people' voted illegally in the election.
The Green Party scam to fill up their coffers by asking for impossible recounts is now being joined by the badly defeated & demoralized Dems
— Donald J. Trump (@realDonaldTrump) November 27, 2016
