Washington(CNN) The Trump administration has unveiled new travel restrictions on certain foreigners from Chad, Iran, Libya, North Korea, Somalia, Syria, Venezuela and Yemen as a replacement to a central portion of its controversial travel ban signed earlier this year.

The new restrictions on travel vary by country and include a phased-in approach beginning next month.

"Making America Safe is my number one priority. We will not admit those into our country we cannot safely vet," President Donald Trump tweeted just after his administration released the details of the restrictions Sunday night.

In a statement Sunday night, the White House called the new restrictions a "critical step toward establishing an immigration system that protects Americans' safety and security in an era of dangerous terrorism and transnational crime."

"We cannot afford to continue the failed policies of the past, which present an unacceptable danger to our country," Trump said in the White House statement. "My highest obligation is to ensure the safety and security of the American people, and in issuing this new travel order, I am fulfilling that sacred obligation."

For the last three months, the administration used an executive order to ban foreign nationals from six Muslim-majority countries from entering the US unless they have a "bona fide" relationship with a person or entity in the country. Those nations included Iran, Syria, Libya, Somalia, Yemen, and Sudan.

Individuals with that "bona fide" exception -- such as a foreign grandparent of a US citizen -- can still apply for visas until October 18. After that date, the new restrictions on travel will begin. The revised travel ban effecting those from six-Muslim majority countries officially expired earlier Sunday, and Sudan was removed from the list of affected countries.

The new list of countries notably includes several non-Muslim majority nations, including North Korea and Venezuela. In most instances, travel will be broadly suspended, while in other cases, travelers will have to undergo enhanced screening and vetting requirements.

For instance, foreign nationals from North Korea are banned, but a student from Iran will be allowed in, subject to "enhanced screening and vetting requirements," according to the President's new proclamation.

However, no current validly issued green cards, visas or travel documents will be revoked.

But unlike the earlier ban, which temporarily limited travel for 90 days, the new restrictions are indefinite and "conditioned based, not timed based," a senior administration official explained on a call with reporters Sunday evening.

The new order additionally provides consular officers with discretion to waive the new restrictions on a "case-by-case basis" if a foreign national demonstrates that denying entry into the US would cause "undue hardship" and he or she does not pose a threat to national security.

Secretary of State Rex Tillerson said in a statement that with the new restrictions, "the President is carrying out his duty to protect the American people."

"The State Department will coordinate with other federal agencies to implement these measures in an orderly manner," Tillerson said. "We will continue to work closely with our allies and partners who share our commitment to national and global security."

Acting Department of Homeland Security Secretary Elaine Duke also issued a statement, saying President's proclamation will allow DHS "to better keep terrorists and criminals from entering our country."

"The restrictions announced are tough and tailored, and they send a message to foreign governments that they must work with us to enhance security," Duke said.

Trump signed the initial travel ban during his first week in office, but it was met with immediate legal challenges, which have continued to hinder implementation of the full scope of the executive order. The administration released a second version in March, which included substantial changes.

The President's latest order was met with swift criticism by the same groups that filed lawsuits earlier this year, including the American Civil Liberties Union.

"Six of President Trump's targeted countries are Muslim. The fact that Trump has added North Korea -- with few visitors to the US -- and a few government officials from Venezuela doesn't obfuscate the real fact that the administration's order is still a Muslim ban," said Anthony D. Romero, executive director of the ACLU. "President Trump's original sin of targeting Muslims cannot be cured by throwing other countries onto his enemies list."

The US Supreme Court is set to hear arguments on the legality of the travel ban next month.