Scottish leader Nicola Sturgeon has had a "sympathetic" hearing in Brussels as she pleaded her case for Scots to stay in the EU, showing how Britain's vote to leave the bloc could splinter the United Kingdom.
But she drew a rebuff from Spain and a mixed response from European officials on Wednesday.
EU leaders met for the first time without Britain.
Outgoing Prime Minister David Cameron flew home after briefing his 27 peers on Tuesday evening on last week's referendum defeat.
Pro-independence leader Sturgeon has said that Scotland, where voters backed staying in the EU by a near 2-1 majority, must not be dragged out of the EU against its will.
She wants to negotiate directly with Brussels to protect the membership rights of Scots - and is open to a new independence referendum if that is the only way to keep Scotland in the bloc.
But Spanish Prime Minister Mariano Rajoy, struggling to prevent the autonomous region of Catalonia from breaking away, said Madrid would oppose any EU negotiation with Scotland.
"If the United Kingdom leaves, Scotland leaves," he said after the first meeting of the 27 EU partners without Britain.
Sturgeon, pointedly referring to Rajoy as "acting" premier following the unclear outcome of Sunday's Spanish election, said she was not at all surprised to hear such "starting positions" from Madrid and she was well aware of the difficulties.
"We are very early in this process," she told reporters, stressing that her priority was to have Scotland's voice heard.
A spokesman for Jean-Claude Juncker, the EU Commission chief who irked some European diplomats by meeting Sturgeon at such a critical time in EU relations with London, stressed that he had listened but would not interfere in British domestic politics.
The 27 EU leaders sent a firm message to London that there would be "no negotiations of any kind" on future trade relations until the UK officially triggers the EU treaty's exit clause.
"This should be done as quickly as possible," they said in a joint statement.
In a clear warning to Britain's Leave campaigners, added at the last minute, the 27 also said that access to Europe's prized single market "requires acceptance of all four freedoms" of movement for goods, capital, persons and services.
Leave campaigners such as former London Mayor Boris Johnson, a favourite to succeed Cameron as Conservative Party leader and prime minister, have said they want free access to the EU common market, but would retain the right to control migration.
Cameron, who campaigned to stay in the EU and announced he would step down by October after he lost last week's referendum, said on Tuesday that Britain's future relations with the bloc could hinge on its willingness to rethink free movement of workers, which he blamed for the referendum result.
There has been a surge in sympathy in many parts of Europe for the 5.5 million Scots, whose strong vote to stay in the EU was overridden by the English, who outnumber them 10 to one.
Britain as a whole voted 52-48 per cent to leave.
But countries like Spain that have dealt with regional separatism are strongly opposed to any direct EU talks with Scotland.
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