By this morning, as many as 3,048,000 people had signed the petition on the official UK Parliament website.
The figure takes it well over the 100,000-signature threshold required to trigger a debate in the House of Commons.
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The development came as some voters who had backed the "Leave" campaign took to Twitter to register their regret -- adopting the #Regrexit hashtag.
A "Leave" voter told the London Evening Standard she would change her vote if given the opportunity.
"This morning the reality is actually hitting in and the regret is hitting in," she said. "I wish I had the opportunity to vote again, simply because I would do things differently."
The petition, started by William Oliver Healey, states: "We the undersigned call upon (the UK) Government to implement a rule that if the Remain or Leave vote is less than 60 per cent, based on a turnout less than 75 per cent, there should be another referendum."
Demand for a fresh vote was so high that it crashed the parliament.Uk website on Friday as the petition was shared widely on social media and new signatures were added at a rate of more than 1,00,000 an hour.
(Only the headline and picture of this report may have been reworked by the Business Standard staff; the rest of the content is auto-generated from a syndicated feed.)