Brexit Secretary David Davis dismissed suggestions that the estimated 3 million EU nationals now living in Britain might be forced to leave, telling Sky News that "I want to see a generous settlement for the people here already. They didn't seek this circumstance, we did."
But he said if a surge of new immigrants trying to "beat the deadline" floods into Britain before it leaves the EU, the Conservative government may have to set a cutoff date.
A desire to reduce immigration from other EU nations was a key reason many Britons voted last month to leave the EU.
Under the bloc's rules, EU nationals can move feely among member states, and Britain has seen its population swelled by hundreds of thousands of new arrivals in recent years.
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Prime Minister Theresa May has been criticised for refusing to guarantee the right of EU citizens to remain in the UK after its EU exit, something that is more than two years away. She says she needs to ensure that hundreds of thousands of Britons living in other EU countries get the same protection.
Davis said he believes Britain will be able to retain access to the single market while opting out of the EU's right to free movement. EU leaders say that's impossible because free movement is a key EU principle, but Davis said "everybody is taking starting positions."
"Of course they are talking tough," he said. "If I was negotiating to buy your house or your car my first offer wouldn't be my final one, would it?"
Scottish voters strongly backed remaining in the EU in the June 23 referendum.
Scottish First Minister Nicola Sturgeon today said she did not rule out Scotland staying both in the UK and in the EU even if the rest of the country leaves the bloc though it's not clear how that could happen.
"We're in uncharted territory, and when you are in uncharted territory with effectively a blank sheet of paper in front of you, then you have the opportunity to try to think things that might have previously been unthinkable," Sturgeon told the BBC.