The petition calling for Brexit to be cancelled by revoking Article 50 has now reached four million signatures.
It was set up on Parliament's website following Theresa May's speech on Wednesday and now has the highest sign-up rate ever recorded.
In Wales, the level of support is varied with the highest signing rates around Cardiff and in rural areas of mid Wales and in Arfon.
Despite the Prime Minister ruling out revoking Article 50, the petition calls on the public to show their support for remaining in the EU .
As of 10am on Saturday, the petition has 4.1million signatures.
People's Vote march: When is it? Where can you join it? How can you get there from Wales?
Despite the website repeatedly crashing due to what is thought to be far-right hackers accessing the system, the petition shows no sign of slowing down.
And thousands of people are due to march through the streets of London on Saturday calling for a People's Vote in a second referendum on leaving the EU.
The People's Vote campaign says: "The final decision should be handed back to the people - because only they can sort this out."
Parliament must consider holding a debate on all petitions that gain more than 100,000 signatures.
It has also outstripped a petition backed by more than 1.8 million people calling for US President Donald Trump not to make a state visit to the UK.
More than four million people signed another petition in 2016 which called for another EU referendum in the event that neither the remain or leave camps achieved 60 percent of the vote.
When asked about the petition, a spokesperson from Number 10 said: "The Prime Minister has long been clear that failing to deliver on the referendum result would be a failure of our democracy and something she couldn't countenance."
On Thursday, EU leaders said Brexit could be delayed from March 29 to May 22 - but only on the condition that MPs vote for Mrs May's deal next week.
If Ms May's deal is rejected in the third "meaningful vote" then the UK would have until April 12 to tell the European Council the way it wants to proceed.
If that is not forthcoming, the EU would prepare for a no-deal Brexit on May 22.
