Lawyers working to prove President Trump’s claims of widespread voter fraud said more than 1.5 million ballots were manipulated in three states — enough to change the outcome of the Nov. 3 election.

Sidney Powell, who is not on the president’s legal team but is filing pro-Trump lawsuits, sued officials in Michigan on Wednesday alleging Dominion Voting Systems software switched tens of thousands of votes for Mr. Trump to presumptive President-elect Joseph R. Biden.

The software manipulation, according to the complaint, was coupled with other fraud such as backdating absentee ballots.

“While this complaint, and the eyewitness and expert testimony incorporated herein, identify with specificity sufficient ballots required to overturn and reverse the election results, the entire process is so riddled with fraud, illegality, and statistical impossibility that this court, and Michigan’s voters, courts, and legislators, cannot rely on, or certify, any numbers resulting from this election,” said the 75-page lawsuit.

Hundreds of pages of exhibits were attached to the complaint, including affidavits from expert witnesses.

The crux of their claim in Michigan is there’s “incontrovertible physical evidence” that the security of the voting machines was jeopardized by the software being connected to the internet, which the lawyers say violated federal election law.

The lawsuit claims the software was developed by individuals with ties to the late Venezuelan dictator Hugo Chavez and has been used to fix elections in other countries.

Dominion Voting Systems, which has a corporate lineage that is linked to Chavez, provided vote-counting software to about two dozen states including Michigan and Georgia.

The Michigan lawsuit points to an expert witness, Russell Ramsland Jr., who said Dominion “is responsible for “the injection or fabrication, of 289,866 illegal votes in Michigan, that must be disregarded.”

David Keshavarez-Nia, another expert witness in both the Michigan and Georgia suits, testified that “hundreds of thousands of votes that were cast for President Trump in the 2020 general election were transferred to former Vice President Biden.”

Dominion is not listed as a defendant in the cases. The company has repeatedly denied wrongdoing or that its machines were manipulated in the 2020 election.

A spokesperson for the company said Ms. Powell’s allegations are conspiracy theories and the Georgia complaint is “baseless, senseless, physically impossible.”

“Sidney Powell’s wild and reckless allegations are not only demonstrably false, they have led to stalking, harassment, and death threats to Dominion employees,” Dominion Voting Systems said in a lengthy statement. “This criminal activity has been duly reported to the appropriate law enforcement agencies, and we intend to hold Ms. Powell, and those aiding and abetting her fraudulent actions, accountable for any harm that may occur as a result.”

Mr. Biden is presumed to have won Michigan, defeating Mr. Trump by roughly 154,188 votes, or 2.8%. The state canvassing board voted to certify the results Monday.

In Georgia, Ms. Powell and her legal team are suing the governor and the secretary of state alleging Dominion software allowed “rogue actors to penetrate and manipulate the software.” The complaint has been shared widely online but is not listed in the court systems’ electronic filings.

Ms. Powell’s expert witness, Mr. Ramsland, concluded “at least 96,600 mail-in ballots were illegally counted,” according to the Georgia complaint.

Officials in the Peach State certified the election for Mr. Biden after a hand recount. Mr. Biden defeated Mr. Trump by about 12,600 votes, or a 0.2% margin. The certification awarded Mr. Biden the state’s 16 electoral votes.

The attorneys general for Michigan and Georgia did not immediately respond to a request for comment on Ms. Powell’s lawsuits.

In Pennsylvania, Trump legal team leader Rudolph W. Giuliani presented witness testimony before an informal hearing with Republican state lawmakers Wednesday.

Retired U.S. Army Col. Phil Waldren, a computer warfare expert, said an estimated 1.2 million votes were altered in Pennsylvania.

His team of analysts focused on anomalies of spikes in election returns. In one instance, about 337,000 ballots he called “loaded votes” had been added to the count on Election Day during a 90-minute span.

“Normally, you would expect to see a smooth curve,” he said. “That big spike that occurred there is a prime indicator of fraudulent votes.”

He noted there appear to be more than 600,000 votes tabulated during the unusual spikes. Out of that figure, he said, roughly 570,000 of those went to Mr. Biden while about 3,200 went to Mr. Trump.

Mr. Trump scored a rare court victory this week when a Pennsylvania court sided with Republicans contesting the state results.

The judge halted further certification of the state’s election results, but the attorney general of Pennsylvania vowed to appeal to the state’s highest court.

However, a federal appeals court on Friday rejected the president’s constitutional challenge which alleged a violation of Equal Protection, saying some Democratic counties in Pennsylvania allowed voters to cure errors on mail-in ballots before Election Day while Republican counties did not afford voters the same opportunity.

“Free, fair elections are the lifeblood of our democracy,” Judge Stephanos Bibas of the 3rd U.S. Circuit Court of Appeals wrote in a 21-page opinion. “Charges of unfairness are serious. But calling an election unfair does not make it so. Charges require specific allegations and then proof. We have neither here.”

The move affirms a lower court ruling issued Saturday.

Judges David Smith and Michael Chagares, both George W. Bush appointees, joined the opinion.

The Trump legal team has vowed to take the case to the Supreme Court.

In Pennsylvania, Mr. Biden is leading Mr. Trump by more than 80,000 votes, or 1.2%.

Nearly three weeks after the election, Mr. Trump appears far from his goal of reversing the projected outcome.

The most likely path to victory for Mr. Trump would have been through Pennsylvania. If somehow he still prevailed there, he would also need to reverse projected losses in at least two other states to reach the 270 electoral votes required to win the White House.

The campaign is fighting to make up ground in Wisconsin, with a recount underway in two of the state’s largest counties.

The Wisconsin recount likely won’t wrap up until just before the state’s certification deadline of Dec. 1. Mr. Trump trails Mr. Biden in the state by about 20,600 votes, or 0.7%.