Also on Saturday, hundreds of thousands of people marched in central London to call for another European Union referendum.
But May herself admits that she is nowhere near to securing the votes needed to finally get her Brexit deal over the line.
At present, the U.K.is set to leave without agreement unless lawmakers approve a divorce deal or choose another path by April 12.
"I think we will see today that there is a mood in the House of Commons to stop us leaving without a deal, even if that means no Brexit", International Trade Secretary Liam Fox told BBC radio. And if the deal is passed, the bloc has agreed to extend the Brexit deadline until May 12.
All the options are back on the table after May's deal twice failed to win parliamentary support by resounding margins.
Organisers of the Put it to the People march said a million people joined the peaceful procession through London, weaving their way from Hyde Park Corner to Parliament Square, spilling over into parks and side streets.
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The petition - which is backed by leading politicians like London mayor Sadiq Khan, Scottish leader Nicola Sturgeon, and a number of Members of Parliament - continues to attract support after hundreds of thousands of anti-Brexit protesters marched through central London on Saturday.
Senior Conservative Party figures were urging May to recognize her weakened political position and leave the prime minister's post.
Watson, the Labour Party's deputy leader, also spoke in support of another referendum, saying it would bring the country back together.
"It is time for the PM to channel the spirit of Moses in Exodus, and say to Pharaoh in Brussels - LET MY PEOPLE GO". "The way to reunite our country is to decide on our future together".
Mrs May will also face Prime Minister's Questions. You're plunging this country into chaos.
Will MPs take full control of the Brexit process?
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At one of the most important junctures for the country since World War Two, British politics was at fever pitch and, almost three years since the 2016 referendum, it was still unclear how, when or if Brexit will ever take place. Article 50 is the exit clause in the European Union treaty.
Among the 27 remaining European Union states, France has the most hardline stance, while Germany and the Netherlands are ready to give Britain more time to break the impasse.
"We need to put a stop to this claim by proving the strength of public support now, for remaining in the European Union", the petition says. "A People's Vote may not happen - so vote now".
An online petition to revoke article 50 exceeded 5 million signatures this weekend, making it the most popular petition ever on the government's website. The protest calls for a public vote on the Brexit outcome, with most supporting a second referendum with remain as an option. "Many people will be strongly opposed to it, but it's a coherent proposition and it deserves to be considered along with the other proposals".
A week prior to Saturday's People's Vote march, a pro-Brexit group began a projected two-week march of their own from Sunderland to London.
Conservative Party legislator George Freeman tweeted Saturday night that the United Kingdom needs a new leader if the Brexit process is to move forward.
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