Conservative lawmakers chose Home Secretary Theresa May and Energy Minister Andrea Leadsom on Thursday to fight a runoff contest for leadership of Britain's governing party.
"I've always said there should be a proper contest and now is the time for me and my team to take my case out to the party members in the country".
The choice of the next prime minister will be made by about 150,000 members of the Conservative Party.
Michael Gove had been in the race this morning, but dropping his vote share to just 46 among members of the parliamentary party means he has now been knocked out of the competition.
The two women are battling it out to replace David Cameron as Conservative prime minister and party leader he resigned following last month's vote to leave the European Union.
Five Conservative contenders had initially been campaigning for Cameron's post, but that number is now down to two, with results expected to be announced on September 9.
The Justice Secretary was out running near his house when he was asked whether he was throwing his weight behind Theresa May or Andrea Leadsom in the leadership contest.
Home SecretaryTheresa May launches her leadership campaign in London, Britain, June 30, 2016.
Mrs Leadsom played a high-profile role in the campaign for Britain to quit the EU.
Leadsom, 53 years old, has been in Parliament since 2010 and is considered less experienced than May. Leadsom had 84 votes.
The new leader will be responsible for leading Britain's exit negotiations with the 28-nation European Union as well as helping to steady the country's government and economy, which has been deeply shaken by markets' reaction to the European Union vote.
He added: "Today we have two strong women candidates going to the country, we will have a woman prime minister".
He welcomed the fact that the United Kingdom would be getting a second female prime minister - after Margaret Thatcher - and called for a "civilised, inclusive, positive and optimistic debate".
"It says to women all over the country "you can get to the top". He said she had the "zap, drive and determination" for the job.
The Bank of England, which warned before the referendum that a Brexit vote would push Britain into a "material" economic slowdown, could cut interest rates as soon as next Thursday.