In a court filing late on Friday, Hawaii's attorney general asked a Honolulu judge to issue an injunction allowing grandparents and other family members to travel to the United States.
The US Supreme Court last month let the ban on travel from six Muslim-majority countries go forward with a limited scope, saying it could not apply to anyone with a credible "bona fide relationship" with a US person or entity.
The Trump administration then decided that spouses, parents, children, fiancés and siblings would be exempt from the ban, while grandparents and other family members traveling from Iran, Libya, Somalia, Sudan, Syria and Yemen would be barred.
Trump said the measure was necessary to prevent attacks. However, opponents including states and refugee advocacy groups sued to stop it, disputing its security rationale and saying it discriminated against Muslims.