Democrats in 23 states and the District of Columbia sued to block the order.
The justices said Tuesday they will take up appeals asking the court to strike down bans on the AR-15 and similar semiautomatic firearms in Connecticut and the Chicago area.
The Supreme Court on Tuesday erased limits on how much political parties can spend in coordination with candidates for Congress and president, striking down a federal election law that is more than 50 years old.
Trump's efforts to restrict birthright citizenship, fire the heads of most independent agencies at will and remove a sitting Federal Reserve governor are among the remaining eight cases the justices are expected to decide this week.
The Supreme Court, in a 5-4 decision, upheld state laws that allow the counting of late-arriving mail-in ballots even if they were postmarked by Election Day.
The Supreme Court has blocked for now President Trump's unprecedented attempt to fire a member of the Federal Reserve Board of Governors, Lisa Cook.