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The first black or Asian prime minister will be a Conservative, David Cameron has said, in a speech on opportunities for ethnic minority Britons.
The prime minister told in audience in south London he looked forward to the day, as he outlined plans to increase the number of ethnic minority Tory MPs.
Mr Cameron also pledged to boost minority ethnic jobs, university places and police recruits by 2020.
Of 306 Conservative MPs elected in 2010, 11 were black or Asian.
Labour had 16 ethnic minority MPs elected in 2010, while the Lib Dems had none.
In that election, the Conservative Party only won 16% of the ethnic minority vote, which has historically favoured Labour. In 2015, it is fielding 56 candidates from black and Asian communities. Labour is fielding 52 ethnic minority candidates.
Setting out his vision to increase the number of black and Asian students, apprentices, entrepreneurs and police and armed forces personnel, Mr Cameron said he was also setting ambitions for the Conservatives.
"In the last Parliament, we increased our number of black and Asian MPs from two, to 11. Now that's not enough, but it's good progress. At this election, there is one party fielding more black and ethnic minority candidates than any other and I'm proud to say, that it's us - the Conservatives."
He said in 18% of "retirement seats", where a Conservative MP was standing down and which "we have a very good chance of keeping", the party was standing a candidate from an ethnic minority. By 2020 - he said he wanted that to reach 20% of retirement seats.
"And why not? We are the first party to have a female prime minister, we were the party of the first Jewish prime minister and I know one day, we are going to be the party of the first black or Asian prime minister," he said.
Pressed on whether he thought Culture Secretary Sajid Javid was in the running to succeed him as prime minister in questions after the speech, he said: "It won't be for me to choose, but the ambition is there and I hope you can sense from me, the excitement is there."
In his speech at the Fairfield Halls, Croydon, Mr Cameron said he wanted Britain to be an "opportunity country" where people from all backgrounds could "make the most of your talents".
He said he wanted to see "ambitious but realistic" targets for black and Asian people - pledging 20% increases by 2020 in the number of jobs, apprenticeships, university places, start-up business loans and police officer recruits from ethnic minorities. In the Armed Forces he pledged an increase of at least 10% "on the way to 20%".
Labour Leader Ed Miliband launched his party's black, Asian and ethnic minority manifesto earlier this month, alongside shadow justice secretary Sadiq Khan - suggesting quotas could be used to increase the number of non-white and working class people in top jobs, including senior civil servants and the judiciary.
They accuse the coalition of overseeing a big rise in the number of young black and Asian people in long-term unemployment.