The order, issued Monday, allows the administration to block asylum seekers from entering the United States until the Supreme Court can assess the legality of a longer-term ban.
Justice Kennedy issued the order after an emergency request from the Justice Department. The order puts a hold on a lower court ruling allowing refugees with a formal assurance from a resettlement agency to enter the United States.
Kennedy called on those suing the government over Trump's travel ban to respond to the latest order by noon Tuesday.
Next month, the Supreme Court will consider whether Trump's travel ban is legal at its core. The ban prohibits travel to the U.S. by citizens and refugees from Iran, Libya, Syria, Somalia, Sudan and Yemen.
The high court has already ruled the Trump administration can legally enforce the travel ban, but cannot keep out those with a "a credible claim of a bona fide relationship" to the United States -- such as those with family members living in the United States, or those with a job or place at a college or university in the U.S.
The ongoing legal wrangling rests on the definition and legal interpretation of "bona fide relationship."
Last week, a federal appeals court ruling -- the ruling since put on hold by Justice Kennedy -- stipulated that the Trump administration could not legally block grandparents or refugees with assurances.
More than 24,000 refugees have already received assurances from U.S. resettlement agencies.