The rules, affecting people from Iran, Libya, Syria, Somalia, Sudan and Yemen, come into force on Thursday.
They were issued after the Supreme Court partially restored President Donald Trump's travel ban.
The controversial executive order had been blocked by lower courts.
According to the new rules, confirmed to the BBC, for the next 90 days those without a close relationship - defined as a parent, spouse, child, son or daughter-in-law, or sibling - will not be able to enter the US.
