The new president is now the head of the US Department of Homeland Security.
But the agency’s chief, Elaine Duke, has yet to publicly announce when her department will return the passports of anyone who has left the country.
Read moreRead moreWhen will I have my passport returned?
Duke told ABC News on Sunday that she was not releasing any specific dates for when the passports would be returned, but would “have to think about it and see how we do it”.
“We are not in a position to make any decisions until we know that we have a plan in place,” she said.
When the government first announced it would return passports in November, Trump had previously claimed that the move would not take “years” and had “no effect” on his travel ban.
On Monday, Duke told ABC’s “Good Morning America” that she would be “very clear” that the decision to return passports was not a “time bomb” but rather an “important step”.
“This is a step that I think the American people have been asking for for quite some time,” Duke said.
“I think it’s a very important step.
We have been pushing hard on this.”
She also confirmed that she will be reviewing all other passports to see if they need to be returned.
“We will have a lot of passports that need to go through a review as well,” she added.
“But we are going to be very clear on this one that this is a very, very important and very important process.”
Duke, a former deputy assistant secretary of homeland security, is now head of DHS’ Office of Intelligence and Analysis, which oversees the department’s counterterrorism efforts.
Duke’s departure will take place during a visit to Washington by US President Donald Trump on Saturday.
The president is expected to address the US public on Sunday.