Sturgeon said she would meet European Parliament President Martin Schulz and planned to set out Scotland's position directly to the European Commission.
London must move fast to take more power after Brexit, Mayor Khan says
Most Scots voted to remain in the EU in last Thursday's referendum.
Denouncing what she described as a vacuum of leadership in London, Sturgeon said three months of political drift until a successor to Prime Minister David Cameron is in place will further damage the UK economy.
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