ATLANTA — A federal judge in North Carolina on Friday rejected an effort by civil rights groups and the Justice Department to block the application of key elements of a Republican-backed state law that curtailed early voting and other opportunities for residents to cast their ballots.

The 125-page written ruling, issued late Friday by Judge Thomas D. Schroeder of the Federal District Court, rejected the plaintiffs’ arguments that the law, one of the most far-reaching in a recent national wave of Republican-backed legislation on voter ID and against voter fraud, would place “disproportionate burdens” on African-American voters hoping to participate in the November elections.

Judge Schroeder, who was nominated by President George W. Bush, acknowledged that given the racism in North Carolina’s past, residents “have reason to be wary of changes in voting law.”

But he cited various ways in which black voters would still have opportunities to get to the polls, even with the less generous ballot access the law affords. For example, one part of the law reduces the period of early voting to 10 days from 17. Judge Schroeder noted that witnesses in last month’s hearing “opined” that the loss of days would hamper get-out-the-vote efforts. “But no witnesses testified that he or she will not be able to adjust operations readily to fit the new early-voting period,” he wrote.