In a separate mail-in ballot case in Pennsylvania, the court declined a second, fast-tracked review of ballot deadlines in that state, where late-arriving ballots can be counted up to three days after 3 November.
Blocking the measure âwould not be in the public interest,â the court said.
The high courtâs decisions are a blow to Republicans who have sought to restrict ballot access during the coronavirus pandemic, while a beleaguered US Postal Service has experienced significant delays in delivering mail.
A favourable ruling for North Carolina election officials and Democrats keeps in place a deadline of 12 November to accept mail-in ballots, as long as they are postmarked by 3 November.
The stateâs Board of Elections argued that the nine-day extension protects âlawful North Carolina voters from having their votes thrown out because of mail delays that the Postal Service had explicitly warned the state about.â
Justice Amy Coney Barrett, the presidentâs newest appointee who was confirmed on Monday, did not participate in the rulings.
Chief Justice John Roberts and Justice Brett Kavanaugh joined the courtâs three liberal justices to rule in the majority in the North Carolina case, while its three other conservative justices â Samuel Alito, Neil Gorsuch and Clarence Thomas â dissented.
Justice Barrett did not participate because she âhas not had time to fully review" court filings, according to court spokeswoman Kathy Arbert.
The Trump campaign and Republican groups had sought to revert the North Carolina deadline for late-arriving ballots to 6 November, arguing that Board of Elections had overruled legislative authority to set election rules.
North Carolina election officials had extended the deadline as part of a legal settlement with union groups, approved under a state judge.
But the courtâs decision not to engage a new Republican appeal in the Pennsylvania case left open the possibility that the court could weigh in after Election Day.
That issue will become critical if the swing state â where a victory for the president or his Democratic challenger Joe Biden could determine who wins the White House â becomes a definitive battleground in the 2020 race.
In a statement, Trump deputy campaign manager Justin Clark said that the court had deferred âthe important issue in the case â whether state courts can change the time, place and manner of elections contrary to the rules adopted by the state legislature â until after" 3 November.
Justice Alito wrote that he âreluctantlyâ concludes that âthere is simply not enough time at this late date to decide the question before the electionâ in that case.
The Alliance for Retired Americans had initially sued for a ballot deadline extension in Pennsylvania.
Its executive director Richard Fiesta said in a statement that the courtâs latest move âis an enormous victory for all Pennsylvania voters, especially seniors who should not have to put their health at risk during the pandemic in order to cast a ballot that will be counted."