Becca Heller, director of the International Refugee Assistance Project, said that of the three countries added: "Chad is majority Muslim, travel from North Korea is already basically frozen and the restrictions on Venezuela only affect government officials on certain visas.
Trump's original travel ban, impacting the six majority-Muslim nations, was roundly slammed for being needlessly discriminatory, haphazard, and divisive.
An administration official of the United States said that the number of travelers from the North Korea to the America was already low.
Officials stressed that valid visas would not be revoked as a result of the proclamation.
It was subject to a range of legal challenges and several large-scale protests, and is due to be considered by the US Supreme Court in October, having been partly reinstated in July.
The US Supreme Court is set to hear arguments on the legality of the travel ban next month.
Trump's original ban that included Iran, Libya, Syria, Yemen and Somalia was highly controversial.
The White House portrayed the restrictions as consequences for countries that did not meet new requirements for vetting of immigrants and issuing of visas.
Grandparents, grandchildren, aunts, uncles, nieces, nephews, cousins, brothers-in-law and sisters-in-law, fiancees or other extended family members were originally not considered to be close relationships and so fell under the ban.
Citizens from the listed nations will face new restrictions on entry to the USA under the proclamation signed by Mr Trump.
The latest restrictions lift the travel ban on Sudan.
On Friday, the president received policy recommendations from acting Secretary of Homeland Security Elaine Duke and was briefed by other administration officials, including Attorney General Jeff Sessions and Secretary of State Rex Tillerson, a White House aide told Reuters earlier in the day.
Unlike Mr Trump's first travel ban, which sparked chaos at airports across the country and a flurry of legal challenges, officials said they had been working for months on the new rules, in collaboration with various agencies and foreign governments.
Even before Mr. Trump's announcement, civil rights groups were upset with the president and said whatever he did would be poisoned by a history of "religious animus" toward Muslims they say he showed during the presidential campaign. The New York Times, the Washington Post and Politico have stories.
"President Trump's original sin of targeting Muslims can not be cured by throwing other countries onto his enemies list".