Lady Warsi – who unexpectedly resigned last week over the government's "morally indefensible" policy on Gaza – said her party is ignoring "electoral reality" by relying on white voters.
Her comments highlight a fundamental split at the top of the party. Warsi is known to agree with Lord Ashcroft, who believes that minority ethnic voters must be won over for the Tories to win future elections.
But Cameron has become much closer to Lynton Crosby, the Tories' election chief, who has argued that it is much more important in the 2015 election to concentrate on winning over potential Ukip voters who are concerned about increases in immigration.
The peer also confronted colleagues who questioned whether she was up to her job, suggesting that Cameron's inner circle did not understand those who had not gone to public school. She said they had dismissed her as a "brown, working-class woman" who was "not good enough to be a minister". They were, she added, some of the "bitchiest" people she had known.
In interviews with the Sunday Times and with the Independent on Sunday, Warsi said that when she was one of Cameron's earliest supporters in 2005 she thought: "This is a guy who gets today's Britain. He's a new kind of Conservative".
"I think the party has shifted since then. The party leadership has shifted since then. I think over time it will be a regressive move because we have to appeal to all of Britain, not just because it's morally the right thing to do … but because it is an electoral reality.
"I will be out there, vocally fighting for an outright Conservative majority," Warsi said. "But the electoral reality is that we will not win outright Conservative majorities until we start attracting more of the ethnic vote."
A study by the cross-party group Operation Black Vote (OBV) last year found the number of seats where black and Asian voters could decide the outcome had rocketed by 70% compared with the 2010 election.
The study suggests that in 168 marginal seats, the ethnic minority vote is bigger than the majority of the sitting MP. The seats extend beyond inner-city areas to include places such as Southampton, Oxford, Sherwood, Ipswich and Northampton.
In the interview, Former Foreign Office minister Warsi called on the Government to "recognise Palestine as a state" and impose an arms embargo on Israel.
She criticised Chancellor George Osborne and chief whip Michael Gove for failing to use their "very, very close" relations with the Israeli government to defuse the crisis.
"What is the point of having that strong relationship if you can't use it to move them to a position which is in their interests and our interests?" she said.
Dismissing Osborne's claim that her resignation had been "unnecessary", she said: "My actions would not have been necessary if he had done what he should have done, which is pick up the phone to people he is incredibly close to and say: 'It's unnecessary for you to meet your ends by taking out power stations, taking out homes, taking out schools and killing kids on beaches'."'
Warsi said the lobbying operation by Israel was "incredibly effective" and raised questions over the influence of party donors.
"I don't blame the [pro-Israel] lobby, I blame the politicians. If you are not capable of being able to decipher between lobbying and fact, and if we are incapable of politicians to see both sides of the argument, then that's a fault that we have."
She added: "I sincerely hope that how the Tory party raises its funds does not have an impact in relation to its policy in government. The national interest should never be subject to the chequebooks of anybody."
In the wake of her resignation, a number of Tory sources were quoted claiming that she was really leaving because she has been a poor minister and forced out of Cameron's inner circle.
Warsi said: "Some of the bitchiest women I've ever met in my life are the men in politics. I am a brown, working-class woman from the north. People have been telling me I'm not good enough since the day I was born."
In a reference to Cameron's inner circle, she added: "I don't hold the fact that someone went to public school against them. I don't hold [against them] the fact that they haven't had the breadth of experience that some of us who didn't go to public school have had.
"I hope that if I can be so understanding about their background and shortcomings, they can be understanding to those of us who haven't had those opportunities."
Her comments attracted criticism. Alec Shelbrooke, the Tory the MP for Elmet and Rothwell, said Lady Warsi had "embarrassed herself" and her criticisms would "quickly fizzle out".
"I think within a week, 'Who was Lady Warsi?' will be the question. She has ended her career in many ways," he told the BBC. He added that by "spreading out into areas of different criticism" she had undermined the real reason for her resignation.
"Isn't it best to step down on a point of principle, but don't you embarrass yourself if you start launching into a tirade about many other things, when you come from a position of having never held elected office?" he said.
Stewart Jackson, the Tory MP for Peterborough and member of the public accounts committee, tweeted: "I worked with Sayeeda Warsi in opposition. Never a team player, over promoted and woefully indulged by people who should have known better."
A Labour party spokesperson said: "Another day, another episode of Tory infighting. The Tories can't focus on the big challenges facing the country because they're looking inwards with David Cameron desperately trying to shore up his own position."
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