The new rules, affecting people from Iran, Libya, Syria, Somalia, Sudan and Yemen, come into force on June 29.
They were issued after the Supreme Court partially restored President Donald Trump’s travel ban.
Donald Trump’s controversial executive order had been blocked by lower courts.
According to the new rules, 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.
The definition of “close” relationships excludes grandparents, aunts, uncles, nieces, nephews, in-laws, extended family and grandchildren.
Also exempt from the new rules are those with business or educational ties to the US.
However, the guidelines specifically state that the relationship must be formal, documented and formed in ordinary course, rather than for the purpose of evading the executive order.
Those who already hold valid visas are not affected. Dual nationals who travel on their passport from the unaffected country will also be allowed entry.
The rules come into effect at 20:00 Washington time.
However, lawyers both for and against the ban have warned that the new restrictions – which will remain in place until the Supreme Court issues a final ruling – could open the door to a flood of legal challenges.
However, the Supreme Court will not be reviewing the case until October – which will mean the 90-day period will be largely done.
The court also approved the 120-day ban on refugees entering the US, allowing the government to bar entry to refugee claimants who do not have any “bona fide relationship” with an American individual or entity.
Donald Trump’s administration has put a cap on the number of refugees it is willing to accept at 50,000, which the State Department said would be reached in the next two weeks.
Rights groups have been fighting President Trump’s executive order for the last five months.
President Trump said the order was needed to stop terrorists entering the US, but critics said it was a ban on Muslims.
The order was first signed in February, but was blocked by the courts. A revised order was halted by a judge in Hawaii just hours before it was supposed to go into force in March.
President Donald Trump called the court’s decision a “victory for our national security.
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