The dismissals of the cases, which all involved plaintiffs represented by lawyer James Bopp and the conservative group True the Vote, occurred in Georgia, Michigan, Pennsylvania and Wisconsin.
The cases are among a group filed by backers of Trump and the president's own campaign as part of an effort to reverse Biden's projected win in the national race for the White House.
Those efforts have largely failed to gain traction and it is not clear that Trump has any chance of overturning his loss through legal actions.
With all 50 states' results projected as of last Friday, Biden has 306 Electoral College votes, 36 more than he needs for victory, compared with just 232 votes for Trump.
But that has not stopped the president both from claiming otherwise and from falsely saying that he won the election.
When asked why the cases were being dismissed, Bopp told CNBC in an email that because of attorney-client privilege, "and because I do not telegraph my next moves, I cannot comment."
It is not clear if Bopp will seek to resurrect the claims, but it is legally possible he and the plaintiffs could do so.
Michigan Attorney General Dana Nessel's office noted that the plaintiffs represented by Bopp in the case there, which sought to invalidate election results in Wayne, Ingham and Washtenaw counties because of claims of voting irregularities and fraud, dropped the action even before serving the lawsuit on the defendants.
"This case was clearly designed to spread misinformation about the security and integrity of Michigan elections," Nessel, a Democrat, said in a statement.
"Our elections have been conducted fairly and transparently and the results reflect the will of Michigan's voters. Any claims to the contrary are wholly without merit," Nessel said.
Kristen Clarke, president and executive director of the Lawyers' Committee for Civil Rights Under Law, said, "We are not surprised that plaintiffs have moved to dismiss their own claims in this case as it confirms the pattern we have seen with these post-election suits — they are littered with baseless allegations that can't be substantiated in a court of law."
"There is no clear or coordinated strategy as these suits continue to crumble," Clarke said in a statement.