Call will now have to be considered for debate in the UK's parliament
A petition calling for another Brexit referendum has gathered over a million signatures.
Signatories are calling for a second EU vote as no campaign attracted more than 60% of the vote, and turnout was less than 75%.
The petition on the UK Parliament website, set up by William Oliver Healey, reads: "We the undersigned call upon HM Government to implement a rule that if the remain or leave vote is less than 60% based a turnout less than 75%, there should be another referendum.”
Any petition with over 100,000 supporters is automatically considered for debate in the UK’s parliament.
The uncertainty caused by victory for the out campaign, which attracted 52% support from voters in Thursday's referendum, has already caused the credit rating agency Moody's to downgrade the UK's long-term issuer and debt ratings from stable to negative.
Support for Brexit was unequal across the UK, with the majority of voters in Scotland and Northern Ireland voting to remain in the EU.
The shock result campaign has prompted the Scottish Cabinet to convene in Edinburgh to discuss the Holyrood administration's next steps.
First Minister Nicola Sturgeon has already warned that a second vote on Scottish independence is now "highly likely" - and described the prospect of the country being taken out of the EU as "democratically unacceptable".
She said today that Scotland will seek to begin immediate talks with Brussels to ensure it remains part of the bloc.