"As President, I can not allow people into our country who want to do us harm", Mr Trump said. "I want people who can love the United States and all of its citizens, and who will be hard-working and productive".
At issue is a 2016 court ruling that determined that Microsoft didn't have to hand over customer data that was stored on computers in another country.
The justices will hear arguments in the case in October, but that will be after what is now a 90-day order expires.
The Supreme Court allows for a 72-hour window before the ban goes into effect.
"We just hope the next time we can get more than a handful of Democratic senators to vote for our nominee to the Supreme Court and to the federal courts", Conway said.
"The high court left in place portions of the lower court injunctions that provide important protections for individuals connected to Washington's families, schools and businesses".
The New York Immigration Coalition, another fierce opponent, said the ruling created more confusion by referring to "bona fide relationship" which "agencies and individuals will struggle to make sense of".
"This order, properly construed, should really allow for only the narrowest implementation of any part of the ban". He has railed against federal judges who have blocked the move.
The Supreme Court's last day before summer recess is Monday, and there is speculation that any news out of the high court could come then.
Republicans, many of whom actively worked against Trump's unorthodox candidacy, have been reluctant to oppose him after he was sworn in as they relished the thought of the first GOP White House and Congress in a decade succeeding in pushing a conservative agenda.
The Executive Orders are complicated.
"President Trump issued this order within his constitutional and statutory authorities to protect the safety of our nation and its citizens", Sen. Sen.
The original measure, issued by executive order in January and nearly immediately blocked by the courts, also included Iraq on the list of targeted countries and had imposed an indefinite ban on Syrian refugees.
Trump's first executive order on travel applied to travelers from Iraq and well as the six countries, and took effect immediately, causing chaos and panic at airports as the Homeland Security Department scrambled to figure out whom the order covered and how it was to be implemented.
He argued it was necessary for national security while the administration reviews procedures for allowing travelers from the Muslim-dominant countries into the U.S. He said in a statement that his "number one responsibility" is to keep Americans safe.
They said that national security is not a " "talismanic incantation" that, once invoked, can support any and all exercise of executive power". Kennedy's departure would allow conservatives to take firm control of the court. The U.S. Court of Appeals for the Ninth Circuit upheld the order. The US Justice Department's lawyer says the president is targeting "Islamic terrorist groups and the countries that sponsor or shelter them", not Muslims.
Conservatives have always cared deeply about the federal bench - atop which sits the Supreme Court - but a series of rulings over the Obama years made Trump's argument even more powerful. "You know why? Supreme Court judges, Supreme Court judges". "What's more hard is if you're coming in on a tourist visa". But immigrant groups said relatively few people try to enter the United States without well-established ties.
In Chin's view, the court's decision means people such as university students and faculty, as well as the mother-in-law of the imam of the Muslim Association of Hawaii, would not be restricted from entering due to religion or national origin. Most Supreme Court cases are decided unanimously, so that assertion would be false as to any justice.