LONDON (Reuters) - Britain would have liked to quickly resolve the issue of post-Brexit rights of European Union nationals in Britain but needs the bloc's agreement on the reciprocal rights of Britons in the EU, Brexit minister David Davis said on Wednesday.

The EU earlier this week rebuffed a call from pro-Brexit British lawmakers for a quick deal on mutual residence rights for British and EU expatriates, saying it had to wait until full-blown divorce talks began.

"If were up to us we would have this resolved in months but we have to get the agreement of the European Union too," Davis said, adding that Britain had a responsibility to protect the rights of its citizens by not agreeing to a non-reciprocal deal.

Davis also said that the outcome of a court appeal over whether parliament's approval is needed to begin formal Brexit talks may impact any bill the government eventually has to introduce.

The BBC reported last month that the government had prepared a bill of just three lines which it believed would be "bomb-proof" against amendments by lawmakers who may try and add conditions to the approval.

"On the question of the court case, it isn't just a yes or no outcome ... the actual nature of the bill may be influenced by the outcome," Davis said.

During the same question session in parliament, junior Brexit minister David Jones said it was "extremely difficult" to see how one part of the United Kingdom could remain part of the single market if the rest did not.

(Reporting by Kylie MacLellan; editing by Sarah Young)