David Cameron has said he hopes to see a British Asian become prime minister in his lifetime.
Speaking at the GG2 awards, which celebrates Asian achievements, he added that there were "too few people from ethnic minorities in top positions".
Culture Secretary Sajid Javid was named the most influential Asian in the UK.
Nobel prize winner Malala Yousafzai, who lives in Birmingham and campaigns for female education after being shot by the Taliban, came second.
One Direction's Zayn Malik was also in the top 10.
Mr Cameron, speaking about Mr Javid, said: "I know we have more to do to encourage true opportunity and diversity in our country but doesn't it say something about our country that in two generations you go from coming to our country with so little to sitting round a cabinet table. That's the sort of country we're building in the United Kingdom."
Mr Javid's father arrived in Britain from Pakistan in 1961 and worked as a bus driver. The culture secretary, who was born in Rochdale, left a career at Deutsche Bank to work in politics.
The prime minister said: "In Britain today there are still too few people from ethnic minorities in top positions".
Mr Cameron said: "The absence is glaring in the boardrooms of FTSE 250, in the chambers of the Houses of Parliament, on football managers' benches, on High Court judges' benches and in our fighter jets, our naval ships and our armed battalions around the world. And I'm clear that this has to change."
He added: "When I hear those terms Your Honour, Brigadier General, Right Honourable, more often I want to hear it followed by a British-Asian name.
"And yes, one day I want to hear that title prime minister, followed by a British-Asian name."
In a jokey reference to Mr Javid, he added: "Just not immediately, if that's OK by you."
Mr Javid was elected as MP for Bromsgrove at the 2010 general election, and was promoted to the cabinet in April 2014 after working as financial secretary to the Treasury. The Conservatives have six Asian MPs, and Mr Javid is the only one with Pakistani heritage.
Labour has 12 Asian MPs and the Liberal Democrats none.
On Wednesday, Baroness Warsi, a former Conservative Party chairman and Foreign Office minister, told BBC Asian Network the Conservatives had effectively given up on attracting Muslim voters at the next election.
She said "a whole series of decisions", particularly the UK's response to this summer's Gaza crisis, were to blame. Lady Warsi resigned from the government in August over Gaza.