Donald Trump's administration has set new rules for visa applicants from six mainly Muslim nations and all refugees, that require a "close" family or business tie to the United States.
The move came after the US Supreme Court partially restored President Trump's executive order that was widely criticised as a ban on Muslims.
Visas that have already been approved will not be revoked, but instructions issued by the State Department say new applicants from Syria, Sudan, Somalia, Libya, Iran and Yemen must prove a relationship with a parent, spouse, child, adult son or daughter, son-in-law, daughter-in-law or sibling already in the US to be eligible.
The same requirement, with some exceptions, holds for would-be refugees from all nations still awaiting approval for admission to the US.
Grandparents, grandchildren, aunts, uncles, nieces, nephews, cousins, brothers-laws and sisters-in-law, fiancees or other extended family members are not considered to be close relationships, according to the guidelines issued in a cable sent to all US embassies and consulates late on Wednesday.
The new rules take effect on Thursday, according to the cable, obtained by The Associated Press.
On Monday, the Supreme Court partially lifted lower court injunctions against Mr Trump's executive order that had temporarily banned visas for citizens of the six countries.
The justices' ruling exempted applicants from the ban if they could prove a "bona fide relationship" with a US person or entity, but the court offered only broad guidelines - suggesting they would include a relative, job offer or invitation to lecture in the US - as to how that should be defined.
Senior officials from the departments of State, Justice and Homeland Security had laboured since the decision to clarify the ruling and Wednesday's instructions were the result.
As far as business or professional links are concerned, the State Department said a legitimate relationship must be "formal, documented and formed in the ordinary course rather than for the purpose of evading" the ban.
Journalists, students, workers or lecturers who have valid invitations or employment contracts in the US would be exempt from the ban.
The exemption does not apply to those who seek a relationship with an American business or educational institution purely for the purpose of avoiding the rules, the cable said.
A hotel reservation or car rental contract, even if it was pre-paid, would also not count.
Mr Trump's initial travel ban in January led to chaos at airports around the world, but because the guidelines exempt previously issued visas, similar problems are not expected.
After a judge blocked the original ban, Mr Trump issued a scaled-down order and the court's action on Monday further reduced the number of people who would be covered by it.
While the initial order took effect immediately, adding to the confusion, this one was delayed 72 hours after the court's ruling.
Would-be immigrants from the six counties who won a coveted visa in the government's diversity lottery - a programme that randomly awards 50,000 green cards every year to people from countries with low rates of immigration to the United States - will have to prove they have a "bona fide relationship" within the US or are eligible for another waiver or face being banned for at least 90 days.
That hurdle may be a difficult one for those immigrants to overcome, as many visa lottery winners do not have relatives in the US or jobs in advance of arriving in the country.
Fifty thousand green cards are awarded annually in the diversity lottery and generally winners only need prove they were born in an eligible county and have completed high school or have at least two years of work experience in an occupation that requires at least two other years of training or experience.