Rishi Sunak on Monday asked the Conservative Party members to unite behind the newly-appointed British Prime Minister Liz Truss, minutes after she defeated him in the leadership contest to succeed Boris Johnson, to steer the country through difficult times.

Sunak, 42, soon after his defeat, took to Twitter to thank everyone who voted for him.

"I've said throughout that the Conservatives are one family. It's right we now unite behind the new PM, Liz Truss, as she steers the country through difficult times," the British Indian former Chancellor tweeted.

Truss polled 81,326 votes, compared to Sunak's 60,399 in an election with a high turnout of 82.6 per cent, with 654 rejected ballots from a total of 172,437 eligible Tory voters.

Truss, 47, is the third female Prime Minister in Britain after Margaret Thatcher and Theresa May.

On Sunday also, Sunak said that if he loses the Conservative Party leadership race, his job would be to support the next government.

In his final interview with the BBC before the results are declared, Sunak said he plans to stay on as a member of Parliament and continue to work for his constituents in Richmond, Yorkshire, if he is defeated by Truss in the race.