(CNN) A petition calling for Brexit to be canceled through the revocation of Article 50 -- the legal process for leaving the European Union -- reached more than 3 million signatures on Friday.
Earlier in the day, the UK Parliament's petitions committee tweeted that the website had crashed and that the rate of signatures was "the highest the site has ever had to deal with."
The petition's text reads: "The government repeatedly claims exiting the EU is 'the will of the people'. We need to put a stop to this claim by proving the strength of public support now, for remaining in the EU. A People's Vote may not happen -- so vote now."
It went viral after a speech by May on Wednesday night when she blamed British lawmakers for the Brexit impasse.
Singer Annie Lennox and actor Hugh Grant were among celebrities who urged their followers to put their names to the petition.
The UK Parliament authorities consider all petitions that get more than 100,000 signatures for debate, but decisions on which ones reach the House of Commons are made by the petitions committee.
A House of Commons spokesman told CNN on Thursday that the committee meets every Tuesday, "so they will likely decide at their next meeting."
However, on Thursday night, asked about the petition and whether she accepted that the mood of the public may have shifted since the Brexit referendum nearly three years ago, May replied that the UK had already voted to leave.
"We didn't say 'tell us what you think and we'll think about it,'" she said.
Asked by a reporter if Brexit would ever happen, she replied bluntly: "Yes, we will be leaving the European Union."
But European Council President Donald Tusk said the UK government "will still have a choice of a deal, no deal, a long extension, or revoking Article 50."
At a tense meeting Thursday, the European Union agreed a delay to the tortuous Brexit process, avoiding the possibility of the UK crashing out of the bloc without a deal on March 29.
The same day, the anti-Brexit petition passed 1 million signatures, accruing nearly 2,000 signatures a minute at one stage.
Several lawmakers have urged people to add their names.
"An issue as big and important as Brexit should not come down to petitions -- that said, if you are frustrated that the PM is just not listening, you can sign here," Scottish National Party leader Nicola Sturgeon wrote on Twitter -- where #RevokeA50Now is the top trending topic in the UK.
On Friday, she tweeted that she would speak at a People's Vote rally in London on Saturday. "Scotland voted to remain in 2016 but people across the UK must have the chance to get out of this Brexit mess," she said. "Whatever Scotland's future -- I hope independent -- it is in all of our interests for UK to be in the EU."
Hundreds of thousands of people are expected to march on Parliament during the rally, including actors Stephen Fry, Keira Knightley and Lena Headey.
The House of Commons petitions committee tweeted that overseas signatures were valid, since "anyone who is a UK resident or a British citizen can sign a petition. This includes British citizens living overseas."
However, the petition will likely not be acted upon. A petition for a second EU membership referendum in June 2016 attracted more than 4.1 million signatures but was rejected by the government.