The partial stay to the injunction does not apply to "foreign nationals who have a credible claim of a bona fide relationship with a person or entity in the United States", which applies to family members with US citizenship or green cards, universities, and companies applying for visas on an employee's behalf.
Regarding the refugee ban, the court held that the same rule applies as to Section 6 (a) - the 120-day halt to the refugee program.
The Supreme Court will review President Trump's travel ban, the court announced on Monday morning. Justices did not address Trump's tweets which have caused legal problems for his administration previously.
America's highest court also granted an emergency request from the White House allowing part of the refugee ban to go into effect.
Trump called the decision "a clear victory for our national security". The executive order also made waivers available for a foreign national seeking to enter the United States to resume work or study, visit a spouse, child or parent who is a USA citizen, or for "significant business or professional obligations". "If we leave it to the folks on the front line, that's just going to lead to more litigation". But the chaotic weekend that ensued ― dozens of people detained at airports and protests nationwide ― also played an early role in defining the Trump administration as clumsy and disinterested in the details and process of policymaking.
As for refugees, the court held that a person seeking refuge in the USA can claim "concrete hardship" - but in the end, if they "lack any such connection to the United States. the balance tips in favor of the government's compelling need to provide for the Nation's security".
That was immediately contested by immigrant rights and civil liberties groups challenging the travel ban, who argued that most would-be travelers can not be barred under the court's compromise ruling.
The Trump administration said the 90-day ban was needed to allow an internal review of the screening procedures for visa applicants from those countries.More news: Liverpool handed transfer boost, but still £20m short of £70m price-tag
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The action isn't expected to set off the kind of chaos seen around the world when Trump signed the first travel ban into effect on January 27.
Those courts had argued the president had overstepped his authority, and that his executive order discriminated against travelers based on their nationality. But that order, too, was challenged by lawsuits, and it was blocked by lower courts before it ever went into effect. Sessions called the threat of terrorism "immediate and real", and said the lower court's injunction "has a chilling effect on security operations overall".
Updated with Trump's statement.
The action Monday is a victory for President Donald Trump in the biggest legal controversy of his young presidency.
"The implementation of the executive order will be done professionally, with clear and sufficient public notice, particularly to potentially affected travelers, and in coordination with partners in the travel industry", the Department of Homeland security said in a statement. "It is not about the campaign or anything else", Toobin added.
Justice Clarence Thomas, joined by Samuel Alito and Neil Gorsuch, said the government has shown it is likely to succeed on the merits of the case, and that it will suffer irreparable harm with any interference.
Thomas expressed concern with the "court's remedy" and said he fears it will "prove unworkable".
The opinion also noted that the entire case might be over and done with by the time the Court hears it in October.
"The fact that Kennedy didn't retire today probably means he won't retire this term", Toobin said.