In progressive rounds of voting, candidates are eliminated until there are only two challengers remaining.
"I have chose to withdraw from the race and work out what is the best way to advance the values that I care deeply about", he told the London Evening Standard newspaper.
The prospect of Boris Johnson running the country looks like an all too inevitable possibility following the first round of votes cast yesterday.
Rory Stewart, who has been and remains the most interesting thing about the Conservative leadership contest, offered up this thought via twitter earlier this week - "I'm beginning to think there are only two candidates who can beat Boris - me, and Boris himself..."
May quit as party leader last week after failing to secure Parliament's backing for her Brexit divorce deal.
A cross-party effort to block a chaotic end to the 46-year partnership failed on Wednesday, potentially leaving more room for manoeuvre for a future premier.
All May's potential successors have said they could find the solution to the Brexit crisis which eluded her. Parliament has indicated it will try to stop a no-deal Brexit which investors warn would hurt financial markets and shock the world economy.
In an interview with Sky News, Stewart was asked to respond to suggestions that Johnson, the former foreign secretary, would go ahead with such a drastic course of action to resolve Brexit. But he is taking flak from other candidates as the only one yet to confirm he will take part in Sunday's Channel 4 debate.
But Thursday's voting revealed each candidate's current level of support.
He said: "The result was far better than expected to be honest".
Three candidates - Mark Harper, Andrea Leadsom and Esther McVey - were knocked out in the first round, in which Mr Hancock, aged 40, received 20 votes.
McVey was pursuing a no-deal Brexit, arguing that the agreement May struck with Brussels keeps Britain too closely tied to the EU.
When questioned on the ability to prepare for no deal over the short period of time before the 31 October cliff edge, Javid admitted that a no-deal Brexit would be "very challenging" for the country, that it would depend on tax stimulus and supply-side stimulus and may lead to job losses.
Javid, Environment Secretary Michael Gove and former Brexit secretary Dominic Raab have enough publicly-declared backers to make it through to the second round.
He also pledged to raise the national living wage to more than £10 an hour.
Meanwhile, Mr Hancock is understood to be considering pulling out of the race to support another candidate with a better chance of winning the 33 votes needed to get past the next round.
The final pair will be put to a vote of the 160,000 members of the Conservative Party from 22 June.
Conservative party headquarters says the postal vote element, when the 140,000 or so party members will pick the country's new prime minister, will be completed in the week beginning Monday 22 July.
The head of the Fire Brigades Union tells James O'Brien that firefighters will never back Boris Johnson for Prime Minister.
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