America's highest court also granted an emergency request from the White House allowing part of the refugee ban to go into effect.
The justices said they would consider in October whether Mr Trump's policy should be upheld or struck down.
Mr Trump seeks to place a 90-day ban on people from six mainly Muslim nations and a 120-day ban on refugees.
The Supreme Court said in Monday's ruling : "In practical terms, this means that [the executive order] may not be enforced against foreign nationals who have a credible claim of a bona fide relationship with a person or entity in the United States.
"All other foreign nationals are subject to the provisions of [the executive order]."