The administration also decided that only refugees who have a personal relationship with a US citizen or organization should be allowed to enter.
Today the justices blocked a later ruling by the U.S. Court of Appeals for the 9th Circuit that interpreted the category of refugees who are eligible to enter the country more expansively than the government would have liked.
The Justice Department's high court filing Monday follows an appeals court ruling last week that would allow refugees to enter the United States if a resettlement agency in the USA had agreed to take them in.
The order was not the court's last word on the travel policy that Trump first rolled out in January. The Justice Department this week asked for an emergency ruling on the Ninth Circuit's decision, but only as it applied to refugees with formal assurances.
White House spokeswoman Sarah Huckabee Sanders said Tuesday night: "We are pleased that the Supreme Court has allowed key components of the order to remain in effect".
Trump signed a revised executive order on March 6 that banned travellers from six Muslim-majority countries - Iran, Libya, Somalia, Sudan, Syria and Yemen - for 90 days and locked out most refugees for 120 days in a move that the Republican president argued was needed to prevent "terrorist" attacks.
Lionel Messi Leads Barcelona Past Juventus with Champions League Brace
Dembele was involved in the move as Messi broke his personal duck against Buffon in the final minute of the first half. Something that went someway to confirming the reasons behind Barcelona's decision - he's more a Messi than a Neymar .
Amnesty International called Tuesday's Supreme Court decision a "devastating blow".
After a series of court defeats for Trump's proposed travel ban, the Supreme Court in June said parts of it could go into effect pending the outcome of the broader case.
The court will hear arguments on the constitutionality of Trump's order next month.
Resettlement agencies do not deal with refugees directly until they get here, the government said in its latest filing.
The Trump administration did not challenge that part of the ruling, and the Supreme Court did not address the question in its Tuesday order, said a New York Times report. Days ago, the Ninth Circuit finally weighed in, siding with the ban's challengers regarding both family members and refugees.
"Refugees with formal assurances are the category of foreign nationals least likely to implicate the national security rationales the government has pointed to in the past", wrote Washington lawyer Neal Katyal, who is representing Hawaii.