Conway told Fox News that the order would take effect on March 16. The first version temporarily closed US borders to all refugees and to citizens from seven mainly Muslim countries.
She confirmed that legal permanent residents and current visa holders would be explicitly exempt from the order, and also indicated that Iraq would no longer be on the list of countries affected.
"Iraq is no longer on the list based on their enhanced screening and reporting measures," Conway said.
It triggered worldwide outrage as well as protests in America and chaos in the first days of its implementation, as people arriving at US airports from targeted countries were detained and sometimes sent back to where they came from.
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Conway did not confirm if the six countries besides Iraq would remain on the no-entry list, but did say Syrian refugees would be treated similarly to refugees from other countries.
The new Republican administration argued the ban was needed to prevent Islamic State and Al-Qaeda fighters from reaching US soil, but it prompted travel chaos and was roundly rejected by immigration advocacy groups.
Critics said the measure targeted Muslims in violation of US law.
A federal judge in Seattle suspended the order, and a federal appeals court in San Francisco refused to reinstate it, leading Trump's White House to come up with a new version, rather than face a lengthy court battle.
Trump criticised the court order suspending the ban as "a very bad decision, very bad for the safety and security of our country. The rollout was perfect."