It overturns an appeals court decision last Friday that said Governor Greg Abbott could not limit drop-off sites to just one per county.
The Texas Supreme Court’s order largely affects the Houston and Austin areas. Opponents of Abbott's order had argued it exceeded the governor's authority and also created an unjust burden on voters in larger counties to travel far distances to drop off their ballots.
The court, however, did not agree with the argument advanced by the plaintiffs. "The plaintiffs complain that limiting early hand deliveries of mail-in ballots to one office per county requires more travel time for some voters. But this ignores the other options for casting their ballots that these voters have," the court opined.
It noted that voters can cast their ballots in person for a longer period of time than usual, with a 45-day window for dropping off ballots before election day on 3 November, as well as the option to mail in their ballots.
The three justices who issued the decision are Republicans, and it has drawn a backlash from the Democratic Party.
Texas Democratic Party Chairman Gilberto Hinojosa said the ruling showed that the “Texas Supreme Court continues to bend the law in any which way to secure Republican political power,” adding that “four outstanding Democratic women” are running for positions on the court this year.
Previously, a state judge in a ruling on 15 October said that Governor Abbott’s limitation on ballot drop-off sites “would likely needlessly and unreasonably increase risks of exposure to Covid-19 infections, and needlessly and unreasonably substantially burden voters’ constitutionally protected rights to vote.” His ruling was upheld by the state Court of Appeals.
Myrna Perez, director of the voting rights and elections programme at New York University’s Brennan Center for Justice, a non-partisan public policy institute which represented the groups challenging Abbott’s order, said she had no plans to take the case to the US Supreme Court.
Tuesday's ruling comes as opinion polls suggested Texas – which has not been won by a Democrat in more than four decades – may now be in reach for Joe Biden, even though Mr Trump won there by nine points in 2016.
Additional reporting by the agencies