Verhofstadt will represent Parliament in the negotiations.
In an interview, the Belgian deputy warned that discussions in the coming months will be “tough and at times, intense.”
He said, “The scale of the talks ahead are unprecedented, but there is unanimity among MEPs that our priority will be to put the rights of citizens first.
“This means moving quickly to agree a reciprocal deal on the rights of UK citizens in the EU and EU citizens in the UK.”
His comments come after the European Parliament last week adopted its Brexit resolution which, he said make clear that any agreement must be subject to the principles of reciprocity, equity, symmetry and non-discrimination.”
Verhofstadt, who said he will approach the talks with “great sadness”, added, “Any degradation of the rights linked to freedom of movement, including discrimination between EU citizens in their access to UK residency rights before Brexit day, would be contrary to EU law.”
The Belgian MEP said that since the UK referendum on its EU membership last June he had received thousands of letters from UK citizens “angry that their European identity is being taken from them against their will.”
These, he said, include a letter from a 15-year-old in the South West of England who was “upset” with his parents and grandparents for voting to leave because he hoped to study in Germany.
Parliament’s resolution, he said, stated that many citizens of the UK have expressed strong opposition to losing the rights they currently enjoy as EU citizens and “proposes that the EU 27 examine how to mitigate this within the limits of Union primary law”.
He added, “I fought hard in Parliament for this provision to be maintained and hope in the coming months to continue to push for such an offer from the EU to British Europeans.”
In the interview, with the Independent newspaper, Verhofstadt, a former Belgian Prime Minister, said, “The EU will defend its interests in discussions with the British government, but I also believe it is important the EU is generous and open to British citizens.”
Meanwhile, European Council President Donald Tusk left no doubt in his draft guidelines for negotiations, released on Friday, that EU rules state that trade deals can only be done with non-members, so that the most the UK can hope for prior to Brexit is an “overall understanding on the framework for the future relationship.”
Tusk met UK Prime Minister Theresa May in London on Friday for talks on Brexit.