A federal judge slapped a temporary restraining order on the open-ended ban before it could take effect this week.
The policy targets Iran, Libya, Syria, Yemen, Somalia, Chad and North Korea, as well as some Venezuelan officials.
Previous iterations of the ban targeted six Muslim-majority countries, but were checked by the Supreme Court.
The state of Hawaii sued in Honolulu to block Mr Trump's third travel ban, which was set to go into effect early on Wednesday.
