Johnson received 126 votes from his fellow Tory MPs, steaming far ahead of Foreign Secretary Jeremy Hunt, who received 46 votes.
Environment Secretary Michael Gove, International Development Secretary Rory Stewart and Home Secretary Sajid David also remain in the race. The five remaining candidates will take part in a BBC debate on Tuesday night.
A third round of voting will take place on June 19.
Johnson was accused of trying to avoid scrutiny by ducking the earlier debates during the leadership campaign — and his opponents are expected to use the Tuesday debate to pile criticisms on the frontrunner.
The voting by MPs will continue until only two candidates remain. At that point, the wider Conservative Party membership will vote to decide who will replace May and take up residence in 10 Downing Street.
Results from the final ballot are expected in the week beginning July 22, after a month of campaigning by the final two candidates.