Sajid Javid, the former Health Minister, and former Foreign Secretary Jeremy Hunt, who lost to Johnson in the 2019 leadership runoff, used interviews in a newspaper to announce their campaigns
The first phase of the contest takes place in Parliament, where Conservative MPs will whittle down the field to a final two by July 21.
But the former education minister faced questions about whether he would even have a chance to steer the economy out of its slowdown, given Johnson's weakening grip on power
Under current rules Johnson is safe from another leadership challenge until next summer. But the executive of the 1922 Committee can change the rules whenever it wants, the British media reports said.
"I don't want to be commemorating another genocide in Europe years from now. We have the power, the world has the power to stop this, and it must act," Javid said.
Matt Hancock quit after he was caught embracing a senior aide in his office, in breach of the social distancing guidelines he helped to create
Javid served as interior minister under former prime minister Theresa May and was chosen by Johnson to become his effective second in command
The domestic Press Association news agency quoted an unnamed source close to Javid as saying Johnson wanted him to sack his team of aides but he refused.
Lone and Parra walked free after being in preventive detention for over 180 days
Javid, 49, is the latest candidate to throw their hat in the ring to enter Downing Street since Theresa May announced her intention to step down as Conservative leader and therefore as British PM