LONDON (Reuters) - Britain hopes to tackle the issue of the future rights of European Union citizens in Britain and Britons living in the EU early on in talks on Brexit, Prime Minister Theresa May said on Wednesday.

On Tuesday, the EU rebuffed a call from pro-Brexit British lawmakers for a quick deal on mutual residence rights for British and EU expatriates, telling them it was up to their government to launch full-blown divorce talks.

May has said she will not kick off formal negotiations this year to give the government time to prepare, but will do so before the end of March next year.

"I would hope that this is an issue that we can look at at an early stage in the negotiations, of course there will be two years of negotiations. I think it is right that we give reassurance to British citizens living in the EU and to EU citizens living here in the UK," she told parliament.

(Reporting by William James and Kylie MacLellan, editing by Elizabeth Piper)