In the first round of voting among Conservative MPs at Westminster, Hancock came 6th with 20 votes, much fewer than Johnson with a flyaway 114 votes.
Announcing his decision, Hancock, the youngest of the politicians to bid for the leadership, did not endorse any of the remaining six contenders, but instead told journalists that he was talking to all of them, Efe news reported.
In an interview in London, Hancock said: "We stand at a defining moment in our country's history and we need to deliver Brexit and then we need to cast forward and bring the country together. That's the goal."
Johnson was given a boost on Friday when he won backing from one of Britain's biggest and best known business tycoons, multimillionaire Lord Alan Sugar.
Sugar announced on his social media site that he "seriously supports Johnson to become the next British Prime Minister".
"The public like him and he will have a good chance of winning the general election in 2021 if not before," said Sugar.
Next week, the list is expected to shrink again when MPs hold their next rounds of voting, starting Tuesday. When only two names remain, a ballot to decide the next leader of the governing Conservatives will be held among the party's around 160,000 members across the country.
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