"This includes seeking clarification from US officials on how NZ dual nationals will be impacted," he said.
The Government was working to make sure New Zealand dual nationals were not disadvantaged, he said, and that all New Zealanders were covered by any exemptions.
Anyone planning travel to the US was advised to contact the US Consulate General in Auckland.
Earlier today, Prime Minister Bill English said the US policy was unclear and the Government had asked for clarification from the US Administration.
It was his expectation that New Zealanders who were also citizens of the targeted Muslim countries would not be affected by the hugely controversial ban, but he could not give any reassurances at this stage.
Despite English's comments, some New Zealanders with passports from one of the targeted countries have reported being denied a visa to the US.
On Friday, Trump ordered a three-month ban on entry into the US by citizens of Muslim-majority countries - Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen - as well as a permanent ban on Syrian refugees and a temporary ban on other refugees.
Australian Prime Minister Malcolm Turnbull said today his US Ambassador had confirmed with the White House that Australian passport holders would "remain welcome to come and go to the United States in the usual way". Speaking on Sky News Australia, Turnbull said the exemption would apply "regardless of their place of birth or whether they are dual nationals".
Turnbull said the exemption was a result of Australia's strong relationship with the US but would not say whether it applied to all Five Eyes members.
English was also asked this morning whether there was a "carve-out" for Five Eyes countries.
"We're checking up on that," he told Radio New Zealand. "I see there's stories that the Canadians do, that the Australians are seeking it.
"The impression I get is that the policy is unclear. But we will be checking up on that."
It was his expectation that someone travelling on a New Zealand passport would be exempt. But he had received no assurance from US officials that this was the case.
So far, the Government has been advised that no one with a New Zealand passport has been caught up in the US policy change.
English rejected assertions that getting a carve-out made New Zealand more complicit in a policy condemned by international leaders.
He reiterated today that he disagreed with the policy, but he did not agree that it was racist.
"I don't believe it's a racist policy, simply. But I'm not here to defend the policy."
His position has been described as "weak" by Labour leader Andrew Little, who wants him to strongly condemn it and raise it with Trump when the two leaders speak on the phone this week.
Speaking on Newstalk ZB, English said his priority was on reassuring New Zealanders, especially Muslims, that this country will remain open to them.
"We don't want them feeling that this kind of global debate is going to somehow upset the arrangements and the spirit that works here."