The White House deliberations come as U.S. embassies and consulates await instructions later Wednesday on how to implement this week's Supreme Court order that partially reinstated the ban after it was blocked by lower courts. The new measures are expected to be implemented Thursday.

The justices' opinion exempts applicants from the ban if they can prove a "bona fide relationship" with a U.S. person or entity. Government lawyers must determine how to define such a relationship. The court offered only broad guidelines — suggesting it would include a relative, job offer or invitation to lecture in the U.S.