The White House has set new criteria for visa applicants from six mainly Muslim countries and all refugees, requiring them to have a "close" family or business tie to the US.
Also exempt from the new rules are those with business or educational ties to the US.
The Supreme Court said in Monday's decision that it would make a final ruling on the executive order in October.
President Trump called the court's decision a "victory for our national security. He said the order was needed to stop terrorists entering the US, but critics said it was a ban on Muslims.
Meanwhile, a number of activist groups have promised to help people caught up in the ban. The New York Immigration Coalition says it plans to be at the city's John F Kennedy International Airport to "monitor the effects of Trump's revised Muslim and refugee ban".