US expands travel ban to include N Korea
Donald Trump issued a presidential proclamation late on Sunday.
"Making America safe is my number one priority. We will not admit those into our country we cannot safely vet," Mr Trump said.
The restrictions on Venezuelans apply only to government officials and their family members.
The three new countries join five others from Mr Trump's original travel ban: Iran, Libya, Syria, Yemen, and Somalia. But the new proclamation removed restrictions that were placed on Sudan.
Mr Trump's original ban was highly controversial, as it affected six majority-Muslim countries, and was widely labelled a "Muslim ban".
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 American Civil Liberties Union rights group said the addition of the new countries "doesn't obfuscate the real fact that the administration's order is still a Muslim ban".
It is not yet clear how the president's new proclamation, which changes several key elements, will affect that legal challenge.
The addition of North Korea and Venezuela now means not all nations on the list are majority-Muslim.