The prime minister also insisted that she will not resign in March after Brexit despite many in her own party expecting her to do so.
Asked about the prospects of quitting after withdrawal or a bid from Mr Johnson, Ms May told reporters on the way to South Africa she intends to stay in her job for the “long term”.
It comes amid growing speculation about a leadership challenge from Mr Johnson, who used his weekly column to trash her proposals for a Brexit deal.
Asked whether she might step down once Brexit is secured, Ms May said: “I’ve been asked before whether it is my intention to lead the Conservative Party into the next general election, I’ve answered that question before: I’m in this for the long term.
“What I’m focusing on doing is delivering what the British people want. The British people voted to leave the European Union and I and the government will be delivering that.”
Pressed on whether she would fight if a leadership challenge was made by the likes of Mr Johnson, she added: “I have said before that I’m in this for the long term.”
She also brushed aside the suggestion that she might face an Australian-style coup after her old Oxford University colleague, Malcolm Turnbull, was deposed as the country’s prime minister in a right-wing plot.
Ms May said politics in Australia had been “certainly active”, but added: “If you look at Australian politics, I think they are rather different from the politics you see in the UK.”
This week Mr Johnson launched an attack on Ms May’s Chequers Brexit plan as a “historic mistake” that will result in national “humiliation” akin to that meted out by the EU on Greece.
The comments are his first substantial intervention on Brexit since his resignation from the cabinet last month and have sparked concern that the Uxbridge and South Ruislip MP, who is popular with party members, is lining up a leadership pitch at the Tory annual conference next month.
Asked during an interview with ITN on Tuesday if she had noticed “how much Boris wants your job”, Ms May replied only: “I was very pleased that Boris was foreign secretary for the period that he was foreign secretary.”
His repeated attacks on her Brexit proposals make it increasingly unlikely that Mr Johnson and his supporters will back it in a Commons vote, making Ms May’s hopes of securing parliamentary backing for her deal harder.
Backbench MPs have long expected Ms May to stand down once Brexit is secured, with one telling The Independent: “She won’t go into the next election.
“They haven’t forgiven her for the last and won’t let her. It’s a matter of when she goes, not if.”
Tory associations have reported high levels of anger at what many members see as the failure of Ms May’s Brexit proposals to fully deliver on the 2016 referendum, and are also reporting a surge in new joiners.
The increase has raised concerns the party is at risk from a Momentum-style takeover from those angry at the deal, with the pro-Brexit group Leave.EU urging members to join the Tories ahead of a future leadership contest.
Mr Johnson’s supporters have said the party should be open to al new joiners, with some also backing rule changes that could ease the ex-cabinet minister’s path to Downing Street.
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