The Prime Minister told Political Correspondent Carl Dinnen she was "in this for the long term" amid speculation about her future in the role.
Mrs May said: "I'm in this for the long term because there's a long-term challenge for the UK".
While some Conservatives continue to see her as an interim leader being kept in place to deliver Brexit, May insisted that she had broader ambitions in office and had no plans to step down.
Number 10 dismissed the claims as "peak silly season".
'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.' Pressed to rule out stepping down before the next election, due in 2022, she replied: 'I'm not a quitter'.
"Yes, there has been an bad lot of speculation about my future which has no basis in it whatsoever", she told Dinnen, adding: "I'm in this for the long term".
The idea that she now wants to spend another five years as party boss will come as a surprise to some of her MPs.
British Prime Minister Theresa May arrived Wednesday in Japan for a three-day visit that is expected to focus on Brexit, trade and security.
Asked by the BBC if it was her intention to lead the Conservatives into the next election - scheduled for 2022 - she replied: "Yes".
The source said there had always been a close and friendly relationship between the United Kingdom and Japan but it has "gone up a level" after the visit.
The Global Times, an offshoot of Communist party mouthpiece the People's Daily, has made an art of ribbing Conservative prime ministers.
May called a snap general election in June, hoping to extend the centre-right Conservatives' slim majority and strengthen her hand going into the Brexit negotiations.
The result sparked speculation of a leadership challenge.
He said: "In fact the ones who manoeuvre probably will not become the leader".