"#Brexit made EU citizens worry about their future in EU27 and UK. EU will be firm on their rights @The3Million #citizensfirst," former French minister Barnier tweeted in English.
Brussels insists that Britain's divorce, including issues such as the rights of more than three million EU nationals in the UK, must be dealt with before any future trade relationship.
Last week Barnier, who was previously a European commissioner, said the amount that the EU says Britain must pay before it leaves, and the future of the border in Northern Ireland, must also be settled.
The European Union meanwhile tweeted a picture of Barnier's negotiating team around a table, with him sitting at the front.
While Barnier was warning Britain, European Council President Donald Tusk and European Commission chief Jean-Claude Juncker stayed silent on the issue during their public appearances on Tuesday.
Tusk is due to receive a letter from British Prime Minister Theresa May on Wednesday formally notifying the EU of its intention to leave, and launching the two-year negotiation process.
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