LONDON (Reuters) - Britain's Brexit minister said he wanted a generous settlement for Britons living in the EU and for Europeans in Britain after the country voted to leave the 28-nation bloc, but declined to fully guarantee the rights of EU citizens.

David Davis, who has said Britain should begin the formal process of leaving the EU by triggering Article 50 in early 2017, said on Sunday that the rights of EU citizens living in Britain should be agreed along with those of Britons in Europe.

"I want to see a generous settlement for the people here already because they didn't pick this circumstance," Davis told Sky News on Sunday.

"We want to do that at the same time as we get a similarly generous settlement for British citizens living in the EU," he said.

Davis said he backed the rights of those living and working in Britain and expected all citizens to be well-protected. However, he suggested that there could be limits if there is an increase in immigration from the 27 remaining EU countries before Brexit occurs.

"One way of dealing with it could be saying OK, only people arriving before a certain date get this protection," he said, declining to fully guarantee the rights of those already in Britain.

Border control was an important theme in the June 23 referendum in which 52 percent of those who voted backed leaving the European Union, however any limitations could be a concern for Britain's largest firms, many of which have spoken in favor of free movement.

Davis, who said his newly created Department for Exiting the European Union currently has 40 staff but will grow to a "couple of hundred", said Britain will now be able to negotiate better trade deals and also keep access to the European single market.

"It will keep its access, but whether it keeps tariff-free access is the issue and ...that is what we are aiming for," he said.

(Reporting by Costas Pitas and Karin Strohecker; editing by Jason Neely)