David Cameron has said he wants to see a British Asian Prime Minister in his lifetime.
Mr Cameron made the remarks at an awards dinner in central London where Sajid Javid, the Culture secretary who is widely tipped as his successor, topped a power list of the most influential Asians in the UK.
Mr Cameron told the GG2 Leadership Awards: "Let us think big about what Britons of all backgrounds can achieve.
"When I hear 'sir', 'your honour' or 'right honourable', I want them to be followed by a British Asian name."
To cheers he added: "One day I want to hear that title 'Prime Minister' followed by a British Asian name."
Earlier Mr Cameron had described Mr Javid, who was in the audience, as "brilliant" during his 10 minute speech, which celebrates achievement among Britain's Asian community.
He said he was "incredibly proud" of Mr Javid "the brilliant Asian man who I asked to join the Cabinet", adding: "Doesn't it say something that in two generations you can go from coming to our country with so little to sitting around the Cabinet table. That is the sort of country we are building in the United Kingdom."
Mr Cameron sat on the top table at the dinner, near Lord Feldman, the Conservative party's co-chairman.
Mr Cameron said: "In Britain today there are still too few people from ethnic minorities in top positions.
"The absence is glaring in the boardrooms of the FTSE250, in the Chambers of the Houses of Parliament, football managers' benches, on High Court judges benches, and in our fighter jets, our naval ships, our armed battalions around the world and I am clear this has to change, not to tick boxes, not to fill quotas but to realise our full potential.
"Britain will only be the best it can be when all its people are able to be all that they can be."
Mr Cameron said his Government had to "remove the barriers that stop people getting on". He pledged it would "attack prejudice in all its forms" and he wanted to "celebrate role models".
Judges of the Power List, compiled by the Asian Media and Marketing Group, said Mr Javid earned the title for being the only Asian voice at the heart of the Government's senior decision-making process and his commitment to "opening the cultural doors for all Britons in the UK".
He pushed 17-year-old Malala Yousafzai, who became the youngest ever Nobel prize winner last month for her work championing global education rights for girls, in to second place after taking the number one spot last year.
Mr Javid said: "Culture is more than a privilege. It's at the core of who we are and how we define ourselves.
"If you're not engaged with our cultural life, you're not engaged with our national life. And in 2014, too many Britons are culturally disfranchised."
The Bromsgrove MP, a former managing director at Deutsche Bank who was grew up in Bristol, has been tipped by some as a potential future leader for the Conservative Party.
The father of four, whose father Abdul arrived in Britain in 1961 from Pakistan with just £1 in his pocket, turned to politics to "give something back" after reportedly earning more than £20 million during his high-flying banking career,
The annual power list, now in its fourth year, named Labour MPs Keith Vaz and Sadiq Khan at number three and seven respectively and Tory MPs Priti Patel and Shailesh Vara at numbers six and nine.
One Direction singer Zayn Malik, recognisable to millions of young music fans across the world, made it to number 10.
The list features 19 women, including BBC Breakfast presenter Naga Munchetty and BBC Radio One presenter Jameela Jamil as well as the director of Liberty Shami Chakrabarti.
Source: The Telegraph.