The officials were meeting to review the situation after British Prime Minister Theresa May officially launched the two-year Brexit divorce process on March 29 and the guidelines Tusk put forward in response two days later.
"The discussion...Showed solid unity and consensus on all the main elements of the draft, including a phased approach to the negotiations," the EU source said.
The source, who asked not to be named, said the 27 believed it was a priority to deal with EU citizens affected directly by Brexit, putting the blame firmly on London.
"But the EU 27 will engage early, seriously and substantially in limiting the damage to citizens upon the UK's leaving."
Some three million EU citizens live in Britain and another million Britons have built lives in the bloc.
May and Tusk have both said they are willing to do their best to resolve this key issue as soon as possible to remove uncertainty.
The officials, widely known as sherpas, will meet again on April 24 to fine-tune the guidelines which the 27 EU leaders are expected to formally endorse at an April 29 summit.
Announcing the guidelines, Tusk said Britain would also first have to make "significant progress" on the divorce terms before any talks on the trade deal sought by May.
London would also have to make progress on paying its part of the bill for the split and ensuring that the border between the Republic and North of Ireland remain open despite it becoming an international frontier after Brexit.
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