Its attorney general says the new version is fundamentally the same as the first, calling it “Muslim Ban 2.0”.
The directive, which takes effect on 16 March, places a 90-day ban on people from six mainly Muslim nations and a 120-day ban on all refugees.
“Nothing of substance has changed: There is the same blanket ban on entry from Muslim-majority countries (minus one),” Hawaii Attorney General Doug Chin said of the new order.
It will bar entry of citizens of Iran, Libya, Syria, Somalia, Sudan and Yemen for 90 days. Iraq, which was included in the first ban, has been taken off the list.
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Mr Chin also said the directive included “same sweeping shutdown of refugee admissions (absent one exception) and lawless warren of exceptions and waivers”, despite the changes made.
As well as exempting approved refugees, the new order lifts an indefinite ban on those from Syria. It will also no longer affect legal US permanent residents, and drops controversial language about giving priority to religious minorities.
Judges ruled that the ban was unconstitutional amid concerns it unfairly targeted Muslims, something the government denied.
Speaking to local news channel Khon 2, Mr Chin said the new ban had the same “nation-of-origin discrimination problems” as the first.
He said this was a particularly sensitive issue in Hawaii because of memories of Japanese internment camps on the Pacific island during World War Two.
In justifying the ban on Monday, Attorney General Jeff Sessions said there are more than 300 refugees under investigation for potential terror offences. But no further details were given.