EU leaders are to meet next week to discuss how to address the impact of Britain leaving the bloc.
But the UK is pushing for an extra week to consider its options.
The bloc has said it wants to discuss the matter at a summit on Wednesday.
In the wake of the Brexit vote, the UK has said the bloc should allow EU citizens to stay and work in Britain, while urging a new trade deal.
European Council President Donald Tusk said he wanted to give Britain a chance to show its commitment to the bloc before agreeing to a new deal.