The Trump administration says the temporary ban is necessary to block terrorists from entering the country, but immigrant advocates charge that it illegally singles out Muslims.
The 90-day ban on visitors from Iran, Libya, Somalia, Sudan, Syria and Yemen, and 120 day ban on refugees, will allow exceptions for people with "close family relationships" in the United States.
But activists said the government has defined that too narrowly, excluding relationships with grandparents and grandchildren, aunts and uncles and others.
And many were concerned about a possibly chaotic rollout of enforcement of the ban, like that in January when it was first announced.
Immigration rights activists and lawyers were waiting to help arrivals at New York's John F. Kennedy International Airport and other airports to be sure those from the six countries with valid US visas were allowed in after the ban went into effect at 8 pm Thursday Eastern time (0000 GMT Friday).
The Department of Homeland Security, which was heavily criticized for mishandling many arrivals when the ban was first attempted in January, promised a smooth rollout this time.
They stressed that anyone with a valid visa issued before the ban begins would still be admitted, and that all authorized refugees booked for travel before July 6 will also be allowed.
"We expect business as usual at the ports of entry starting at 8 pm tonight," said a DHS official. "Our people are well prepared for this."
The Trump administration insists the ban was necessary to protect the country from terror threats, and to give immigration authorities more time to tighten vetting of travelers and refugees.
"As recent events have shown, we are living in a very dangerous time, and the US government needs every available tool to prevent terrorists from entering the country and committing acts of bloodshed and violence," a senior administration official told reporters Thursday.
Trump claims political victory
But implementing it, even with exceptions, was also claimed as a political victory by Trump, after Federal appeals courts twice blocked his order saying it violated Constitutional protections of religion and overshot his own presidential powers.
According to guidelines issued by the State Department, people with "close family relationships" would be exempt from the ban. It defined that to include parents, spouses, children, sons- and daughters-in-law, siblings and step- and half-siblings.
But "close family" does not include grandparents, grandchildren, aunts, uncles, nieces, nephews, cousins, brothers-in-laws and sisters-in-law, fiances and any other "extended" family members, the guidelines say.
People with formal relationships with a US entity -- who have for instance been offered a job or been accepted to study or lecture at a university -- will also qualify for visas during the ban. But a hotel reservation, even if already paid for, does not qualify.
Democratic legislator Bennie Thompson blasted the government for a "lack of preparation and transparency" in putting into place the ban.
"Just hours before the president's unconstitutional and misguided travel ban takes partial effect tonight, administration officials briefing Congress were unwilling or unable to provide meaningful answers about how they determined whom the ban would affect," said Thompson, the senior Democrat on the House Homeland Security Committee.
Rama Issa, executive director of the Arab American Association of New York, said the government is redefining what a family is.
"I was raised by my grandparents, so the idea of grandparents not being part of a family is very foreign to me," she said at Kennedy International, preparing to help arrivals after the ban takes effect.
"I'm engaged to get married. I have family who lives in Syria today -- not only my father, but my aunts and uncles who I would love to be at this wedding, and unfortunately are not going to be able to be here."
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)