The future rights of UK nationals living in the EU and EU nationals living in Britain is one of the issues the EU wants to settle in the first stage negotiations. Only then will it move on to talks over the future trading relationship.
In a letter updating a committee of lawmakers from Britain's upper house of parliament on the negotiations, Davis said the EU was only offering restricted residency rights to Britons.
"Their offer only guarantees residence rights in the member state in which a British national was resident at the point of our exit from the EU. It does not guarantee the holder ... any right to onward movement within the EU, for example to work or study in a neighbouring member state.
"We have questioned whether this is consistent with the principle of reciprocity, and also with the Commission's desire to protect rights currently enjoyed under EU law. This will be the subject of further discussion in due course."
The EU Commission had no immediate comment on Davis's letter.
After the first full round of talks last month, chief EU negotiator Michel Barnier said there was "a fundamental divergence" between the two sides on how to protect the rights of expatriates after Brexit.
Britain set out in June proposals to allow current immigrants from the EU to retain healthcare, work rights and other benefits that are more generous than those given to migrants from elsewhere.
It said those who had lived in Britain for five years by an as yet unspecified cut-off point could acquire "settled status", similar to permanent residency. Those more recently arrived would be allowed to stay until they achieved this status.
The next round of Brexit talks is due to take place in the last week of August.
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I don’t see a problem here. EU citizens resident in the will be given a resident status in the UK. Why should brits be given EU wide resident status?