The petition has had the highest rate of sign-ups on record, adding more than two million signatures in 24 hours.
There are now more than 5million signatures on a petition calling for Article 50 to be revoked, making it the most popular petition ever submitted on the Parliament's website.
Petitions that get 10,000 signatures will receive a government response, while those that pass 100,000 are debated in parliament.
The previous record was a bid to hold a second referendum on the UK's exit from the European Union, which garnered a total of 4 million and 150,000 signatures in 2016.
Theresa May ruled out cancelling the countdown during her visit to Brussels on Thursday, telling reporters: "I do not believe that we should be revoking Article 50".
On Sunday, Chancellor Philip Hammond told Sky News's Sophy Ridge a second referendum was a "perfectly coherent position" which "deserves to be considered along with the other proposals".More news: Jacinda Ardern orders Royal Commission Inquiry into Christchurch terror attack
The House of Commons petitions committee has refused to comment on its security checks but said the Government Digital Service uses "a number of techniques" to identify suspicious signatures and bot activity. Margaret Anne Georgiadou, 77, started the online petition in February.
The website requires signatories to tick a box confirming they are a British citizen or United Kingdom resident and provide a name, email address, country and postcode.
Brexiteer Julia Hartley-Brewer wrongly suggested people could sign the petition a few times with the same email address for instance, as the Express claimed most signatories were outside the United Kingdom.
Mrs May said, "They voted in 2016, they voted to leave".
"Asking for a friend (16,141,241 of them)". Former Ukip leader Nigel Farage re-joined the March to Leave when it set off from Linby, near Nottingham, on Saturday morning.