Brexit minister David Davis says the EU has proposed only allowing Britons living in the bloc to remain in their country of residence once a deal between the two parties has been rubber-stamped.
The future rights of UK nationals living in the EU and EU nationals living in Britain is one of the issues the bloc wants to settle in the first stage of negotiations.
Only then will it move on to talks over the future trading relationship.
In a letter updating a committee of MPs 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," he said.
"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 European Commission, the Brussels-based executive arm of the EU where a special team is negotiating with London on behalf of the other 27 states, said divorce negotiations should start with addressing the uncertainty caused by Brexit.
"That includes the financial settlement and the uncertainty that surrounds the rights of EU citizens in the UK and of UK citizens in the EU," a spokeswoman said.
"This should be agreed on the principles of continuity, reciprocity and non-discrimination," she said, adding that the triggering of the exit clause by Britain "does not change the right to free movement".
She added: "Nor should it affect the rights of citizens who have made life choices on the basis of EU law and EU membership."
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.