According to the Press Association, a spokesperson for the UK’s Department for Exiting the European Union (EU) said the country’s “first aim” was to move ahead on securing the rights of EU citizens in the UK and UK citizens living in the EU.
“We want to end the anxiety facing four million citizens,” he said.
“That has always been our first aim and that is what we will do. That is why we are pushing ahead with negotiations on Monday.”
So far Theresa May has refused to unilaterally guarantee the residency rights of EU nationals living in Britain until the EU agrees reciprocal rights for Britons living in other EU countries.
The one-day meeting between EU chief negotiator Michel Barnier and UK Brexit secretary David Davis will take place “as part of the sequenced approach to the talks” which the EU has said aim to progress withdrawal arrangements before any talks on trade can begin.
Barnier told the BBC a "constructive" opening to negotiations was crucial in setting the tone for what he hoped would be an "orderly" process.
"We must first tackle the uncertainties caused by Brexit - first, for citizens but also for the beneficiaries of EU policies and for the impact on borders, in particular Ireland," he said.
British expats living in the EU are worried what effect Brexit will have on their state pensions and reciprocal healthcare which gives them the right to go to any member state and receive public healthcare which is then claimed back from the UK government.
Last month, a report by the UK health charity Nuffield Trust warned that tens of thousands of expat pensioners across the EU may return to the UK if the country fails to secure reciprocal healthcare rights after Brexit, with the cost of treating them on the NHS likely to double to £1bn ($1.28bn, €1.14bn).
How many British expats in the EU?
About 900,000 British citizens are living in other European Union countries, according to research by the UK’s Office for National Statistics, with Spain home to the largest number at 308,805.
A third of them – 101,045 – are aged 65 or over. The next most popular countries for British citizens living abroad are France, with 157,062, Ireland, 112,090 and Germany, 96,200.
Meanwhile, there are 3.15 million EU nationals live in the UK, with the largest group represented being Polish nationals at 916,000.