The delayed start to the travel ban follows a Supreme Court ruling allowing some of Trump's executive order to take effect pending a full hearing on the case later in the year.
The policy came into effect at US consular offices worldwide at 8 p.m. in Washington (0000 UTC Friday).
"We have worked closely with our inter-agency partners to ensure that this is an orderly rollout," a State Department official said in telephone briefing with reporters, adding that officials expected things to "run smoothly."
Officers from the State Department, the Department of Justice, and the Department of Homeland Security reportedly all participated in the briefing at the launch of the travel ban.
The key agencies involved in implementing the travel ban are yet to issue any public statements on how the ban - with all its exceptions - will be implemented.
Supreme Court decision
The Supreme Court announced earlier in the week that it would hear arguments in the case in October, and meanwhile lifted part of the injunctions used by lower courts to block the latest order issued by Trump in March.
The court allowed the federal government to enforce the 90-day ban on issuing new visas for individuals from Iran, Libya, Somalia, Sudan, Syria and Yemen who have "no connection to the United States at all."
The Supreme Court decision did concede that Trump's order in both categories could not be enforced against people with "bona fide" business and family relationships in the United States, because their exclusion could injure the rights of those US residents. Trump described the decision as "a clear victory for our national security."
Confusing family relationships
The State Department specified that the exceptions include family reunions, whereby parents, parents-in-law, brothers and sisters, half-siblings, step-siblings, daughters-in-law and sons-in-law can still be issued visas to visit US residents.
The exceptions do not extend to grandparents, sisters-in-law or brothers-in-law, aunts and uncles, or nieces and nephews, according to the State Department. Fiancés were initially included as part of the ban, before State Department said just minutes before the order came into effect that they would qualify as a "bona fide" family relationship, based on the Supreme Court ruling.
Exemptions to the ban also include people with formal business relationships with a US entity who have been offered a job or accepted to study or lecture at a university. Those with existing visas are also protected and should not encounter major issues when entering the country.
Despite these guidelines, questions remained over the exceptions to the ban.
Karen Tumlin, legal director of the National Immigration Law Center, decried the new rules, saying they would "slam the door shut on so many who have waited for months or years to be reunited with their families."
Even before the new ban was implemented Thursday, the state of Hawaii asked a federal judge to clarify the Supreme Court's ruling, saying the US government intended to violate instructions by barring people with close family relations to US nationals from entering.
Halt to refugee arrivals
New approvals for admissions of refugees from all countries will be halted for 120 days.
An official told the Reuters news agency that a "formal assurance" from a US resettlement agency to a refugee would not in and of itself be enough to exempt a refugee from the 120-day ban.
The order means that the US is unlikely to settle many more refugees beyond the 50,000 cap set by Trump. According to US officials, some 49,000 have already entered the US this fiscal year.
President Trump had first ordered the travel ban in January 2017 as one of his first acts after his inauguration, following up on campaign promises to secure US borders against the threat of terrorism.
The original ban set a 90-day halt on travelers from the six aforementioned countries plus Iraq, while the government was to review its vetting procedures. Federal courts stepped in and stopped the travel ban in its tracks based on complaints that the president had overreached his executive powers and violated the Constitution by essentially focusing his order on Muslims.
A revised ban - which notably removed Iraq from the country list - was also blocked in March, forcing the administration to appeal to the Supreme Court.
ss/jm (AFP, dpa, Reuters)