Pending its decision, the court stayed the operation of the EO in part, while permitting other parts of the EO to go into effect.
"We grant the government's applications to stay the injunctions, to the extent the injunctions prevent enforcement of [Mr Trump's executive order] with respect to foreign nationals who lack any bona fide relationship with a person or entity in the United States", the court said.
Mr Trump tweeted: "Great day for America's future Security and Safety, courtesy of the U.S. Supreme Court".
Some lawyers also said the vagueness of the bona fide standard was licence for the Trump administration to interpret it broadly.
By the time the court hears arguments in October, the administration has said it expects to have concluded all the measures it laid out to improve the screening system for those entering the USA from the six countries.
The restrictions, signed by President Donald Trump within a week of his inauguration in January, were quickly challenged and nearly immediately blocked by federal courts. When that relationship is with an individual, the court made clear, it must be a close family member.
Jamal Abdi, policy director for the National Iranian American Council, said most Iranians who visit the United States have relatives here or are coming to work or study.
The justices ruled Monday in an unsigned opinion they would hold a full hearing on the case in October. Trump's decision to freeze travel from certain countries and suspend refugee arrivals could have been within his purview, if he had implemented his order responsibly.
But the decision nonetheless marks a win for the Republican leader, who has insisted the ban is necessary for national security, despite criticism that it singles out Muslims in violation of the USA constitution.
But previous rulings had argued that the president overstepped his authority and that his executive order was discriminatory.
The limited reinstatement of the travel ban is anticipated to take effect on or about June 29, 2017.
The nation's highest court took a more nuanced view, allowing the ban on travelers from Libya, Iran, Somalia, Sudan, Syria and Yemen and the suspension of the refugee program.
Because the executive order was stopped by lower courts, travelers from the six countries have been entering the United States by following normal visa procedures. The court's decision sets the stage for a major ruling on the breadth of presidential power.
The order bans citizens of six Muslim-majority countries from entering the United States.
Who will determine a "bona fide" connection? The court will also hear oral arguments on the case in the fall.
Mr Trump first signed an executive order on this issue in January.