His comments came after former prime minister Sir John Major said he would seek a judicial review if Mr Johnson tried to suspend parliament to force through a no-deal Brexit.
If anybody were to attempt to shut down Parliament in order to carry out a course of action which Parliament is known to oppose, that would be very serious indeed.
House Speaker John Bercow has said it is "blindingly obvious" that the next prime minister would not be able to sideline parliament, adding: "Parliament will not be evacuated from the centre stage of the decision-making process on this important matter".
"The idea of proroguing parliament is utterly and totally unacceptable from any British parliamentarian or democrat", said Major, who is backing Johnson's rival Jeremy Hunt for the leadership but said he was speaking in a personal capacity.
That prompted Mr Hunt to accuse him of avoiding direct answers and relying on nothing more than optimism to win a new deal from the European Union, or to leave without a deal which would hurt businesses across Britain.
May told the Daily Mail in an interview published Friday that the job of prime minister is not about power but about public service. "It's evident that if you have the disruption that comes from a no-deal Brexit there will be people that will lose their jobs".
"I think, somehow, Alex, much as I love the USA, much as it would be a dream job for me in many ways, I'm afraid I've got to stick around in case they drop the ball again".
"I will continue to argue vigorously against a no-deal Brexit".
AQuestion Time special with the two Conservative leadership candidates "now looks unlikely to go ahead".
The outgoing PM, who will be exiting Downing Street to make way for Hunt or Johnson by July 23, said she felt a "mixture of pride and disappointment" and that despite having to go earlier than she wanted, she had been the "right person" for the job and was "immensely proud" of what she had accomplished.
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