Free movement of people from the EU to the UK could be extended after Brexit, Theresa May has suggested.
The prime minister said there would be an "implementation" phase once an exit deal had been struck, with business and governments needing a "period of time" to adjust to any new restrictions.
The government insists Brexit will give the UK greater control of its borders.
But Labour said Mrs May's comments showed she was trying to "downplay expectations".
BBC deputy political editor John Pienaar says the comments clearly left open the possibility of free movement continuing, at least temporarily.
Speaking to journalists during her visit to Jordan and Saudi Arabia, the PM was pressed on what would happen if there was a transitional phase after a Brexit deal is reached.
She said: "You've used the phrase transitional phase; I have used the phrase implementation period.
"Once we've got the deal, once we've agreed what the new relationship will be for the future, it will be necessary for there to be a period of time when businesses and governments are adjusting systems and so forth, depending on the nature of the deal - but a period of time when that deal will be implemented."
However, Mrs May said the government would still be in charge of its immigration policy.
"What is crucial for the British public, what was part of the vote that they took last year, was that they want to ensure that we have control of our borders and control of our immigration," she said.
"That's exactly what we will do when we come out of the European Union."
A change of tone
By John Pienaar, BBC deputy political editor
Nagging questions about the future after Brexit continue to follow the prime minister at home and abroad.
The shape of future immigration policy is high on the list. One key change, Mrs May said, would be that borders and immigration policy would be under British control.
That clearly left open the possibility of free movement continuing, at least temporarily.
She did not endorse talk in Brussels of a transitional period of maybe three years. But the tone of ministers discussing immigration policy has changed.
Suggestions of a sharp cut in EU migration after Brexit has given way to caveats and qualification.
The rhetoric and slogans of the EU referendum and its aftermath have passed - now Mrs May and her ministers are preparing the ground for the give-and-take and compromises involved in their mission to deliver success and stability outside the EU.
Mrs May was also asked about when she expected a new trade deal to be finalised with the EU, after European Council president Donald Tusk made clear one could only be agreed with non-members - meaning the UK would have to wait until after it had left.
She told Sky News: "There's obviously a legal situation in terms of how the EU can conduct trade negotiations.
"I'm clear that by the point at which we leave the EU, it's right that everybody should know what the future arrangements, the future relationship, that future partnership between us and the European Union will be.
"That's the sensible thing, it's the pragmatic way to look at this, and I believe that's what we will do."
Labour's Brexit spokesman, Paul Blomfield, said: "It is less than a week since the prime minister triggered Article 50, and it seems every day brings another broken promise.
"They need to spell out the transitional deal that will be in place, to stop the economy falling off a cliff edge without new agreements in two years' time."