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Scottish First Minister Nicola Sturgeon said that Scotland has delivered an "unequivocal" vote to remain in Europe.
"I welcome that endorsement of our European status," she said adding that the Scottish people "see their future as part of the EU".
Angus Robertson, the Westminster SNP leader, has told STV the UK is facing a "constitutional crisis", with Leave closing in on victory in the EU referendum.
"If it is the case that Scotland has voted to remain in the European Union and we are watching the potential of Scotland being taken out of the European Union, the diametrically opposed position to what we were promised, this will bring about a constitutional crisis in the UK," he said.
The timescale for another Scottish referendum will be dictated by when and if David Cameron begins negotiations for Britain to withdraw from the EU, Alex Salmond has said.
The former Scottish First Minister and remain supporter told ITV News's Tom Bradby that another vote on Scottish independence could take place within two years.
"From when that starting gun is fired, it's a two-year period," Mr Salmond said.
"So whatever that period is - two years, two-and-a-half years, that would have to be the timescale of the next referendum because what you would want to do is remain in the European Union while the rest of the UK moved out."
Mr Salmond pointed out that the SNP's manifesto said if Scotland was "dragged out" of Europe against the will of the Scottish people, then the Scottish parliament should have the right to hold another independence referendum.
Scotland's First Minister Nicola Sturgeon has praised Scotland for supporting the 'Remain' campaign with "a clean sweep" north of the border.
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The party leader said her MPs may be in a position to act as deal makers - and they would refuse to allow an exit from the EU.
Scotland's First Minister said her government will seek 'immediate discussions' with Brussels to "protect Scotland's place in the EU".