He called on the party to return to its traditional values of low tax, strong policing and not to follow the policies of the left-wing Labour Party.
Labour leader Jeremy Corbyn wrote to May on Friday informing her that the Brexit talks, which began on April 3, had "gone as far as they can" due to the instability of her government and its refusal to fundamentally shift its position. Labour has feared any compromises on issues such as workers' rights would be torn up by May's successor. Investors are wary of the prospect of prolonged political turmoil and the risk that a hardliner who favors a no-deal Brexit could end up in charge.
Such a step would complete the first stage of Britain's divorce from the European Union and set it on the path she had laid out.
Johnson quit as foreign minister previous year over the government's Brexit strategy and has been an outspoken critic of the divorce deal May struck with Brussels last November.
May has said she will resign once a Brexit deal is approved and make way for a new leader to guide the United Kingdom through the next stage in the process, which will determine the country's future relationship with the EU.
That deadlock has deepened this week with the breakdown of the cross-party talks and intensifying pressure on May from within the Conservative Party to quit.
Boris Johnson's slightly muted declaration that he would run for the Leadership of the Conservative Party, and therefore, the country will bring some comfort to many seeking an end to Theresa May's regime.
May's deal has faced opposition from those who wish Britain was remaining in the European Union and want a second referendum, as well as those on the right of her party who believes that it leaves Britain handcuffed to the bloc.
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The poll for The Times found that he is viewed as the leader most likely to triumph in a general election, with 70 per cent believing he would be victorious.
Pro-Brexit Conservatives are furious that Britain hasn't yet left the European Union, nearly three years after voters backed Brexit in a referendum.
Several members of May's Cabinet have already started unofficial leadership campaigns, including Johnson, who told a business event Thursday that "of course I'm going to go for it".
"Will consider any new proposals from government on Brexit".
May plans to put her original Withdrawal Agreement to lawmakers for a fourth time in early June, and votes could also be held on a set of alternative options.
Pro-Brexit politicians think the withdrawal agreement keeps Britain bound too closely to the EU's rules, while pro-Europeans have raised alarm about the economic and geopolitical ramifications of leaving the world's second-largest economy by Gross Domestic Product.
"The position of the government has become ever more unstable and its authority eroded", Corbyn said in a letter to May on Friday.