Johnson told fellow Conservatives that if the country does not leave the European Union as scheduled on Oct. 31, the party will be wiped out by angry voters.
"Delay means defeat," Johnson told supporters at a campaign rally. "Kick the can again and we kick the bucket."
Johnson is the bookies' favorite and has won the backing of many pro-Brexit Conservatives by promising Britain will quit the EU by Oct. 31, with or without a divorce deal. The audience for his launch included prominent members of the fervently pro-Brexit wing of the party, whose opposition to May's deal helped end her premiership.
Johnson, a former mayor of London and foreign secretary, is a popular but divisive figure, and rivals have criticized his low-profile campaign. He hasn't given any television interviews or held public events, in a bid to avoid gaffes that could hurt his chances.
Johnson took six questions from journalists Wednesday, but avoided answering directly when asked to confirm his previous account of trying cocaine when he was a student, and when asked whether he had the right character to lead the country.
The tousle-headed politician has a string of past blunders and provocations that have included calling Papua New Guineans cannibals and accusing people in Liverpool of "wallowing" in victimhood. Last year he was criticized for comparing Muslim women who wear face-covering veils to "letter boxes."
An unrepentant Johnson said people felt alienated because politicians had a habit of "muffling and veiling our language."
"Of course I am sorry for the offense I have caused, but I will continue to speak as directly as I can," he said.
In votes starting Thursday, the 313 Conservative lawmakers will narrow the field of 10 candidates down to two, who will be put to a vote of about 160,000 party members nationwide.
The winner, who will become Britain's next prime minister, is due to be announced in late July.