If an immigrant from any one of the countries articulated by the president in the order has a legal relationship with a person, school, business or other entity in the US, they will not be banned.
Trump said last week that the ban would take effect 72 hours after being cleared by courts.
The nine justices, who will hear arguments in the case in October, said the ban could now be enforced for travelers from the targeted countries "who lack any bona fide relationship with a person or entity in the United States".
"Given that preserving national security is "'an urgent objective of the highest order, '" the Court stated that, "To prevent the Government from pursuing that objective by enforcing [the ban] against foreign nationals unconnected to the United States would appreciably injure its interests, without alleviating obvious hardship to anyone else".
The same rules apply to all refugees because Mr Trump's travel ban also included a 120-day suspension of the U.S. refugee resettlement programme. The Trump administration has been fighting back against lower court rulings that have struck down the travel ban.
"For example, a nonprofit group devoted to immigration issues may not contact foreign nationals from the designated countries, add them to client lists, and then secure their entry by claiming injury from their exclusion", the court wrote.
In allowing key parts of President Trump's travel ban to take effect, the high court-with help from Trump's man Neil Gorsuch-upended the conventional wisdom on the case.
"The court went out of its way to not tip its hand as to how it will rule on the ultimate issue, which is whether the president has the power to do this".
Unsurprisingly, Trump championed the Supreme Court's decision Monday as a vital tool to be used in the interest of national security: "Today's ruling allows me to use an important tool for protecting our Nation's homeland".
The move prompted protests and legal challenges which blocked implementation of the ban. The effect on refugees could be greater because they are less likely to have family, school or business relationships in the United States. Refugees from these countries would be denied entry for a period of 120 days.
The ruling was also met with a chorus of bravos from Trump supporters who say it will make America safer, with additional vetting of who gets in and who doesn't.
"Like all countries, USA authorities have the final decision as to who enters their territory".
The justices will hear full arguments in October in the case that has stirred heated emotions across the nation and pointed rebukes from lower courts saying the administration is targeting Muslims. To left-leaning analysts, it's a clever political compromise that still protects numerous refugees and foreign nationals who would've been excluded by the ban.
"President Trump's Muslim ban violates the fundamental constitutional principle that government can not favor or disfavor any one religion", said Devon Chaffee, executive director of the ACLU of NH.