After the June snap election triggered speculation May would be deposed, Johnson also sent a WhatsApp message defending her, saying: "Folks we need to calm down and get behind the prime minister".
The leader of the plot to oust Theresa May has been told to "shut up" by former leadership hopeful Andrea Leadsom, as the party desperately attempts to put on a show of unity at the end of yet chaotic week.
Mrs Leadsom is said to have left Cabinet colleagues stunned after she made remarks during a two-hour meeting to discuss the Prime Minister's Florence speech last month.
Several Tory MPs have already openly called for Johnson's dismissal after he joked Libya could be a tourist destination once the "dead bodies" there were removed.
In it he said: "We have JUST HAD AN ELECTION and people are fed up with all this malarkey".
Shapps, who said he had the support of around 30 MPs, said his intention had been to quietly gather signatures after May's party conference speech was derailed by a series of mishaps, but that the whips had taken the "extraordinary" step of making it public by naming him as the ringleader in a story in the Times.
Mr Shapps was reportedly later added to the group on the app, simply so colleagues could make clear their fury at his move.
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"One minute journalists are accusing me of being an ice maiden or a robot, then they claim I'm a weeping woman in dire need of a good night's sleep", she said, adding: "I am not someone who gives up".
However, cabinet ministers, including Environment Secretary Michael Gove and Home Secretary Amber Rudd, were among those who backed the prime minister on Friday.
She later told BBC Radio 4's Any Questions that Mrs May "has the absolute support of her entire Cabinet and of her party".
He also cast doubt about the level of support Mr Shapps claimed to have, pointing out they had "not spoken out or let their names be known".
"I think if the plotters were serious, they would be led by someone a bit more serious", she said. I really don't think that having a bit of a cold. when you are trying to make a speech changes the fundamentals of whether Theresa May is the right person to lead the country.
'I think there's an bad lot of people in our party that need to settle down'.
Former minister Ed Vaizey was the first MP to publicly suggest Mrs May should quit on Thursday, telling the BBC: "I think there will be quite a few people who will now be pretty firmly of the view that she should resign".