After taking similar legal action in other key battleground states, the Trump campaign has filed a lawsuit in Nevada.
Among the complaints are some that have already been put before the courts and were unsuccessful, US broadcaster ABC News reports - including an attempt to stop ballots being counted.
Without providing evidence, the suit claims: "Irregularities have plagued the election in Clark County, including lax procedures for authenticating mail ballots and over 3,000 instances of ineligible individuals casting ballots."
Trump has repeatedly alleged electoral fraud and irregularities in states in which either Biden is leading, or Trump's lead is shrinking.
In Nevada, where Joe Biden is currently ahead, Donald Trump supporters had until now been calling for the ballot count to continue - believing that further votes would be uncovered for Trump.
Meanwhile, Republican Senator Lindsey Graham, a close ally of Donald Trump, has pledged to donate $500,000 (£380,000) to help fund the Trump campaign's lawsuits.
"The allegations of wrongdoing are Earth-shattering," Graham, who was re-elected in South Carolina, told Sean Hannity in an interview with Fox News, without providing any details, reports BBC.
"I'm here tonight to stand with President Trump - he stood with me, he's the reason we're going to have a Senate majority," he said.
The money donated to Trump's legal team will come from Graham's own campaign funds, the Associated Press reports.