If a withdrawal deal could be ratified within the first three weeks of May, the United Kingdom could still avoid participation in that month's European Parliament elections and leave the EU in June, she said.
Addressing cheering supporters, Ms Rees-Mogg said it was not a decision she had taken lightly after years loyally supporting the Tories.
While the European Union is urging Britain to use the extra time wisely, the British parliament broke Thursday for a two-week recess.
However, the pro-EU and pro-Brexit parties are eager to run for elections, which was view as a way to express strong disagreement views on the bloc.
"This party is not here just to fight the European elections", he said. On Friday, Nigel Farage launched the campaign of his newly formed Brexit Party.
Farage was a co-founder of UKIP, the UK Independence Party, which went on to become a powerful voice in the campaign for Britain to end its membership of the EU.
"The fightback begins here", said Farage, who formerly led the U.K. Independence Party and has sat in the European parliament since 1999.
The former UKIP leader said the existing parties should "fear the electorate" who feel "betrayed" by the failure to deliver European Union withdrawal nearly three years after the 2016 referendum.
"I never wanted to seek this extension", May said.
Conservative Brexiteer MP Jacob Rees-Mogg's sister Annunziate Rees-Mogg is among the new party's candidates for the May elections.
"I know the whole country is intensely frustrated", she said.
Labour Leader Jeremy Corbyn has been engaged in talks with the government since at least last week seeking to break the Brexit impasse, but hasn't been satisfied with what he's heard back from the Conservatives.
While the Foreign Office has done a fantastic job in keeping Britons up-to-date on Brexit the politicians have failed us in London.
The idea of a second Brexit referendum is very likely to be put before Britain's parliament again although the government remains opposed to any new plebiscite, the British finance minister said on Friday (April 12).
If the talks fail, May says she will let Parliament vote on a variety of Brexit alternatives, including the Government's proposed deal, in hope something can command a majority.
It nearly doesn't matter what that is - a cross-party deal that allows a Brexit deal to pass, a second referendum to break the deadlock, a general election that finally sees off May.