Iraq - which was covered in the previous seven-nation order - has been removed from the new one after agreeing to additional visa vetting measures.
The directive, which includes a 120-day ban on all refugees, takes effect on 16 March.
The previous order, which was blocked by a federal court, sparked confusion at airports and mass protests.
Presented as a means to strengthen national security against terror threats, it was blocked by the courts and effectively remains on hold.
The new order was unveiled by Secretary of State Rex Tillerson, Attorney General Jeff Sessions and Department of Homeland Security Secretary John Kelly.