David Cameron has pledged there will be 'no limit' to the number of students from India who can study in the UK and then stay on to find work.
The Prime Minister wants to develop a new 'special relationship' with the emerging superpower and said potential students simply needed 'a basic English qualification and a place at a British university'.
Mr Cameron's change of heart comes as he begins a campaign to win over voters of Indian origin.
He was stung by evidence from Tory pollsters showing that being non-white is the single biggest reason why people don't vote Tory - far outweighing income and social class - even though many Asians share Conservative values.
He will reinforce his message with a trip to India next week billed as the biggest trade trip ever organised by Downing Street.
In interviews with Asian television stations in the UK yesterday, Mr Cameron revealed his love of cricket and hot curries and sought to convince Asian voters that the Tories share their values of family and hard work.
But he also went out of his way to encourage Indians to come to the UK - an offer that contrasts with years of Tory rhetoric about restricting immigration.
He said: 'There is no limit on the number of students who can come from India to study at British universities, no limit at all. All you need is a basic English qualification and a place at a British university.
'What's more, after you've left a British university, if you can get a graduate-level job there is no limit to the amount of people who can stay and work, or the time that they can stay at work.'
Existing Home Office rules mean that any student who obtains a graduate-level job, defined as a post with a salary of at least £20,000, can stay in the UK
But some Tories criticised Business Secretary Vince Cable after a previous trip to India in 2010 when he complained that restrictions on Indian immigrants were too tight.
Mr Cameron admitted last night that he had failed to 'properly communicate' the policy to Indians.
He added: 'Now we need to take that message out to talented young people in India and say if you want to make that choice, Britain will be incredibly welcoming.
'We have 40,000 Indian students in Britain, I'm really proud of that.'
The Prime Minister is set to make a speech on race relations in the next two months in which he will seek to overturn the view that the Tories are a racist party which has lingered since the days of Enoch Powell.
Mr Cameron is also considering whether to make an apology for the worst aspects of the British Empire.
On a trip to Pakistan in 2011, he conceded that Britain was 'responsible' for many of the world's problems including the divisions over Kashmir.
Yesterday he again referred to that 'history' but declined to intervene in talks between India and Pakistan.
Others are encouraging him to visit Srebrenica, where 8,000 Bosnian Muslims were slaughtered in 1995, to help the Tories connect with Muslims in the UK.