The nine justices, who will hear arguments in the case in October, said the ban could now be enforced for travellers from the targeted countries "who lack any bona fide relationship with a person or entity in the United States".
The State Department said it would begin enforcing the travel ban "in a professional, organised and timely way" within 72 hours, in line with a memorandum signed by Trump earlier this month.
"All other foreign nationals are subject to the provisions of [the executive order]".
But the court's ruling also underscores the view that Trump was overreaching when he banned all travel into the United States by certain refugees and foreign nationals from six countries.
"As President, I can not allow people into our country who want to do us harm", said Trump in a statement.
Yes. The definition of a "bona fide relationship" is not clear yet, according to opponents of the ban.
The high court will now decide whether applying Colorado's public accommodations law to compel the baker to create "expression"- a wedding cake - violates his constitutionally protected Christian beliefs about marriage.
Mr Trump has hailed the high court's order as a "clear victory for our national security".
Three of court's most conservative justices dissented in part.
"We will keep those traveling to the United States and partners in the travel industry informed as we implement the order in a professional, organized, and timely way", a State Department spokeswoman said. For example, if a vacationer has a reservation at a hotel in the United States, does that qualify as a "bona fide relationship"? If that is the case, then we should be making every effort to create connections and ties through robust global exchange and travel, and we call on the administration to make clear in its guidance that prospective students and scholars should not be afraid to seek admission to the United States regardless of their current ties. People from Libya, Iran, Syria, Sudan and Yemen would be barred from entering the US unless they meet the formal relationship exception.
A couple blocks away, waiting for the bus downtown, Trump supporter Billy Harrison says he feels safer after Monday's court decision. In the meantime, the justices reinstated the Trump travel ban, but made exceptions for people with close family relationships in the U.S., students attending colleges here, workers and lecturers offered jobs in the U.S. But for travelers or refugees without ties in the U.S., the Trump administration ban is now in effect. This means that people from six countries and refugees who have a family, business or other relationships cannot be banned from entering. The travel ban's persistence as a legal issue suggests that the Trump administration is contemplating more than temporary restrictions on travel and refugee admissions.
By the time the Supreme Court hears arguments on the travel ban, its 90-day life will have expired and the Trump administration will need to give the court a reason as to why it should be continued.