The rules, affecting people from Iran, Libya, Syria, Somalia, Sudan and Yemen, come into force on Thursday, according to the BBC.
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.
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 United States.
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 (00:00 GMT).
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.
But 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 United States, allowing the government to bar entry to refugee claimants who do not have any “bona fide relationship” with an American individual or entity.
Mr 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.
The Supreme Court said in Monday’s decision: “In practical terms, this means that [the executive order] may not be enforced against foreign nationals who have a credible claim of a bona fide relationship with a person or entity in the United States.
“All other foreign nationals are subject to the provisions of [the executive order].”
Rights groups have been fighting President Trump’s executive order for the last five months.
He said the order was needed to stop terrorists entering the US, but critics said it was a ban on Muslims.
It 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 Trump called the court’s decision a “victory for our national security.