Mr Trump issued an executive order on March 6, calling for a 90-day ban on travellers from Libya, Iran, Somalia, Sudan, Syria and Yemen, and a 120-day ban on all refugees to enable the government to implement stronger vetting procedures.
"Today's unanimous Supreme Court decision is a clear victory for our national security", said Trump in a White House statement.
Trump said the ban will come in effect within 72 hours of the court's decision.
The March 6 order called for a 90-day ban on travellers from Libya, Iran, Somalia, Sudan, Syria and Yemen and a 120-day ban on all refugees entering USA to enable the government to implement stronger vetting procedures.
The Supreme Court did not change the duration of Trump's travel ban.
"As president, I can not allow people into our country who want to do us harm", Trump said in a statement.
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Footage showed families, fearing a return to Isil rule, leaving by vehicle and on foot against a backdrop of rising black smoke. They said that the extremists had intentionally detonated bombs within the mosque and in the 800+-year-old minaret next to it.
But that is not the policy Trump actually tried to implement, and relying on his campaign comments to conclude that his executive order is a "Muslim ban" in disguise leads to unusual results. For persons with "close familial relationships" and for those with documented relationships with employers and schools, for instance, the injunctions against the order shall remain in effect pending final resolution of the cases.
"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".
The ruling also said it would permit a 120-day ban on all refugees entering the United States to go into effect. "As for entities, the relationship must be formal, documented and formed in the ordinary course, rather than for the objective of evading [the travel ban]", the Supreme Court decision said. "The answer the Supreme Court gave yesterday is that some parts of the order are going to be constitutional and some parts are going to be unconstitutional".
That would include students who have been admitted to a U.S. school and workers who have accepted an offer of employment from an American company, the court said. As of May 31 of this year, 46,403 refugees have been admitted into the USA - close to the cap of 50,000 that the Trump administration put into place. "It is true that the travel ban is allowed to go into effect, but the Supreme Court substantially narrowed who could be denied entry". He said his group has no idea how the administration plans to judge family relationships and a hard line could mean a significant number of Iranians will be kept out the country for the time being. The new technology comes as the airline is facing a tough travel environment with the implementation of the travel ban, as well as the ban on large laptops and electronic devices. The court's opinion explained the kinds of relationships people from the six countries must demonstrate to obtain a USA visa.
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That court also put a hold on separate aspects of the policy that would keep all refugees out of the United States for 120 days and cut by more than half, from 110,000 to 50,000, the cap on refugees in the current government spending year that ends September 30.