Donald Trump's long-awaited but slimmed down travel ban on travellers from six Muslim-majority nations and all refugees is now in place but is being criticised by immigrant and refugee groups who say the definition for those exempt from it is too narrow.

The advocates say language barring grandparents, grandchildren and fiances from obtaining visas to travel while the ban is in place, despite a Supreme Court ruling this week that people with a "close familial relationship" should not be included in the ban.

The ruling allowed parts of President Donald Trump's March 6 executive order to go into effect after lower courts had blocked it.

The ban is now in effect in the US along with a 120-day ban on refugees. Grandparents, grandchildren and fiances of people in the US will be barred from getting US visas during the 90-day period of the ban, according to guidelines issued by the State Department.

The new guidance for travellers from Iran, Libya, Somalia, Sudan, Syria and Yemen, would also prevent the entry of refugees who do not have close family in the United States.

"They're supposed to be interested in saving as many refugee lives as possible. Instead they've come up with a very narrow interpretation that effectively suspends the refugee program except for those with very close family connections," said Chris George, director of Integrated Refugee and Immigrant Services, a refugee resettlement agency in New Haven, Connecticut.

The court exempted from the ban travellers and refugees with a "bona fide relationship" with a person or entity in the United States from the ban. As an example, the court said those with a "close familial relationship" with someone in the United States would be covered.

Karen Tumlin, legal director of the National Immigration Law Center, said the administration's guidance "would slam the door shut on so many who have waited for months or years to be reunited with their families."

Asked how barring grandparents or grandchildren makes the United States safer, a senior U.S. official did not directly answer, instead pointing to Trump's guidance to pause "certain travel while we review our security posture."

The US government expects "things to run smoothly" and "business as usual" at US ports of entry, another senior US official told reporters.