Trump ordered the new restrictions to replace an expiring measure that had locked him into political and legal battles over what critics alleged was an effort to block Muslims from entry into the country since he took office in January.
"Making America Safe is my number one priority. We will not admit those into our country we cannot safely vet," Trump said in a tweet.
Sudan, one of the six majority-Muslim countries on the original travel ban, was removed from the list. Under the new restrictions, eight nations now have complete or partial blocks on travel to the United States.
Full travel bans were placed on nationals from North Korea and Chad, while the restrictions for Venezuela were limited to officials from a long list of government agencies and their families.
Other countries included in the ban were Iran, Libya, Somalia, Syria and Yemen.
In a presidential order, Trump said the action was needed to press the countries to improve procedures for identifying their nationals and sharing information with the United States.
In addition, he said, the list was created to "advance foreign policy, national security and counterterrorism objectives."
"These restrictions are both vital to national security and conditions-based, not time-based," a senior administration official said, noting that countries can be removed from the list if they can rise to US traveler vetting standards.
Officials stressed that while Iraq was not included on the new list, it was deeply deficient in security vetting of immigrants and travelers to the United States.
But Baghdad is a close ally and supports the presence of large numbers of US troops and civilian officials. But acting Secretary of Homeland Security Elaine Duke recommended tough restrictions on travelers to the United States.
Not A 'Muslim Ban'
"Religion, or the religious origin of individuals or nations, was not a factor," a senior government official told reporters.
"The inclusion of those countries, Venezuela and North Korea, was about the fact that those governments are simply not compliant with our basic security requirements."
Chad was added to the list even though Trump's order called it "an important and valuable counterterrorism partner."
But the order noted the presence in Chad of several designated terror groups like the so-called Islamic State, Al-Qaeda and Boko Haram.
Nevertheless, "Chad does not adequately share public-safety and terrorism-related information," it said. And, the order added, the country failed on one "key" but unspecified criterion used in a broad review of countries for the travel ban.
North Korea, locked in a dangerous face-off with Washington over its nuclear weapons program, was added, the order said, because Pyongyang "does not cooperate with the United States government in any respect."
Venezuela, in a political and economic crisis due to its embattled, increasingly oppressive regime, was listed for a limited ban.
The order placed a prohibition on officials from state agencies responsible for weak security vetting and lack of cooperation with the United States, including the interior and foreign ministries and the main police and intelligence services.
The bans for the five countries from the previous 90-day order, which expired Sunday, would immediately continue under the new order. For North Korea, Chad, and Venezuela, the restrictions will be implemented starting October 18.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)