Plans to rush through a special summit on April 6 of the leaders of the remaining 27 countries are now off the table because there is not enough time, the source said.
"The UK notification on 29 March does not leave sufficient time to prepare a European Council on 6-7 April to adopt the Brexit guidelines," the source told AFP on condition of anonymity.
The source said that there was "no specific date set yet for the European Council at 27, but we expect to need approximately four to six weeks to prepare and consult with the EU 27 member states."
EU President Donald Tusk, who is responsible for calling summits, said he would issue the draft guidelines within 48 hours of Britain triggering its exit.
The timing of the summit would partly depend on the French presidential election, which has two rounds on April 23 and May 7, other European sources added.
Formal talks between Britain and the EU must then wait for member states to approve more detailed negotiating rules and give an official mandate to European Commission Brexit negotiator Michel Barnier, officials said.
Actual negotiations might not start until June, they added.
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