The decision to come out fighting followed reports that she was preparing to stand down the day before Britain leaves the European Union in 2019.
In a series of interviews during a visit to Japan, Mrs May set out her plan to fight on, promising to deliver social reforms that will give the country a “brighter future”.
Asked if she intends to fight the next election, she said: “Yes. There’s been an awful lot of speculation about my future which has no basis in it whatsoever.
“I’m in this for the long term. There’s a real job to be done in the United Kingdom. It’s about getting the Brexit deal right, it’s about building that deep and special partnership with the European Union, but it’s also about building global Britain, trading around the world.
“Yes, dealing with injustices that remain inside the United Kingdom, but also going out around the world ensuring that we can do those trade deals which bring prosperity to our economy and bring jobs to the United Kingdom.”
Pressed to rule out stepping down before the next election, due in 2022, she replied: “I’m not a quitter.”
After the disastrous June election that saw Mrs May lose the Conservative majority, the humbled premier told backbenchers she would continue to serve as long as the party wanted her to.
But the Prime Minister struck a more strident tone as she visited Kyoto, Japan’s ancient capital, for meetings with counterpart Shinzo Abe.
Mrs May said she was “here for the long term and it’s crucial, what me and my Government are about is not just delivering on Brexit, we are delivering a brighter future for the United Kingdom”.
She set down the marker after a summer of speculation about her leadership, and mischief-making including suggestions that colourful backbencher Jacob Rees-Mogg is ideally placed to take the helm.
But Mrs May’s declaration comes just two years after her predecessor, David Cameron, insisted he would remain in post even if he lost the EU referendum, only to quit weeks later when his worst fears were realised.
The PM will spend Thursday in Tokyo for a series of meetings and visits, including attending the Japanese National Security Council, the first European leader to do so.
She will also visit the headquarters of the Japanese maritime self-defence force, where the flagship aircraft carrier Izumo is based, and will be briefed by UK and Japanese personnel on board.
Jon Trickett, shadow minister for the Cabinet Office, said: “The Prime Minister is deluding herself.
“Neither the public nor Tory MPs believe her fantasy of staying on till 2022. Theresa May leads a zombie government.
“The sooner the public has the chance to vote out her and her government the better for our country’s future.”