The new, open-ended restrictions follow a review of information sharing by other countries, the White House said.
Iran, Libya, Syria, Yemen and Somalia remain under the travel ban. Sanctions previously placed on Sudan were lifted.
In a proclamation, Mr Trump said the countries in the list had "inadequate" security protocols. "I must act to protect the security and interests of the United States and its people," he said in the document, issued late on Sunday.
Mr Trump's original ban in March 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 was due to be considered by the US Supreme Court on 10 October, having been partly reinstated in July.
But on Monday the Supreme Court postponed the October oral arguments, and instead called upon all parties challenging the White House to resubmit briefs to the court on whether the case should be dismissed.
