Three G.O.P. candidates for Michigan governor will stay off the ballot, the state’s Supreme Court rules.

The Michigan Supreme Court on Friday denied requests by three Republican candidates for governor to be restored to the August primary ballot, after state election officials found that their campaigns had submitted forged signatures.

The candidates — James Craig, Perry Johnson and Michael J. Markey Jr. — did not meet the total number of signatures necessary to qualify for the ballot after thousands of the signatures on their nominating petitions were found to be fraudulent, though officials said there was no evidence the candidates had knowledge of the widespread cheating effort.

In three separate 6-to-1 rulings, the Michigan justices said they were “not persuaded that the questions presented should be reviewed by this Court.”

“There is nothing here meriting our further time or attention,” Chief Justice Bridget Mary McCormack, a Democrat, wrote in an order on Mr. Johnson’s challenge.

The decision leaves Republicans greatly weakened in their primary for governor in a key battleground state, and strengthens the hand of Gov. Gretchen Whitmer, a Democrat who is up for re-election.

Michigan was viewed as a top 2022 target by Republicans eager to make inroads in the state, which President Biden won in 2020 by more than 150,000 votes. Ms. Whitmer became a target of the Republican base for her stewardship of the state during the early stages of the coronavirus pandemic.

Mr. Craig, a former Detroit police chief, was considered an early front-runner for the nomination. He raised more than $2 million last year, outpacing his Republican rivals, though he trailed Ms. Whitmer in fund-raising.

Now, it is unclear whether Mr. Craig and his Republican counterparts have a path forward, possibly through write-in campaigns, or if they will be forced to abandon their bids. Several G.O.P. candidates have characterized their disqualification as politically driven as they fight it in court; in all, five Republican contenders for governor have been declared ineligible over forged petition signatures.

Representatives for Mr. Craig and Mr. Johnson, as well as for the Michigan Republican Party, did not immediately respond to requests for comment.

Garett Koger, a lawyer for Mr. Markey, lamented the court’s decision in an email on Friday night, but did not say what the campaign’s next steps might be.

“We respect the court’s decision and understand it was under an extreme time crunch, but we are disappointed it didn’t take Mr. Markey’s case up and rule on the merits,” Mr. Koger said. “It’s our position Michigan’s voters should have had a robust field of candidates this August rather than it being narrowed by an unchecked bureaucracy.”

The ruling came as the state faced a Friday deadline for completing ballots for the Aug. 2 primary, which state election officials have said is crucial for programming computers and preparing absentee ballots.

In its review last week of the nominating petitions, the Michigan Bureau of Elections issued a stinging criticism of the methods used by the candidates’ campaigns to collect signatures and the operatives working for the candidates.

“The bureau is unaware of another election cycle in which this many circulators submitted such a substantial volume of fraudulent petition sheets consisting of invalid signatures,” the bureau said. It also clarified that it saw no evidence that the candidates had any knowledge of the fraud.

Election officials said they had identified 36 people who had submitted fraudulent petition sheets consisting entirely of invalid signatures. On May 23, 19 candidates learned that they had not met the signature requirement to get onto the ballot, including three Republicans and one Democrat seeking House seats, and 10 nonpartisan candidates seeking judicial posts.

More than half of the 21,305 signatures submitted by Mr. Craig’s campaign were rejected, leaving him with 10,192 valid signatures, the bureau said in its report, which noted that little effort had been made to vary handwriting.

“In some cases, rather than attempting varying signatures, the circulator would intentionally scrawl illegibly,” the bureau said of the petitions for Mr. Craig. “In other instances, they circulated petition sheets among themselves, each filling out a line.”

The elections bureau rejected 9,393 of the 23,193 signatures submitted by Mr. Johnson’s campaign, leaving him with 13,800 valid signatures. Some of the fraudulent signatures represented voters who had died or moved out of the state, the bureau said.

Deadlocked along party lines, with two Democrats supporting the disqualification and two Republicans opposing it, the canvassing board on May 26 upheld the bureau’s decision to exclude the candidates. A candidate must get a majority of votes from the board’s four members to be certified for a spot on the ballot.

Jonathan Brater, Michigan’s elections director, told the canvassing board during its meeting that the fraud was so blatant that the petitions were referred to the state attorney general for criminal investigation.

“It’s a terrible thing for our state and it’s an attack on our election system,” Mr. Brater said.