Theresa May should publicly acknowledge that Islamophobia is a problem in the Conservative Party, former party chairman Baroness Warsi has said.
Parts of the party had been "in denial" about the issue and a "clear statement" was needed about what was to be done to tackle it, she told the BBC.
The Muslim Council of Britain has urged the Tories to launch an independent inquiry into alleged Islamophobia.
A Tory spokesman said it took all incidents of Islamophobia seriously.
The Muslim Council of Britain has repeatedly demanded an investigation, and says there are now "more than weekly incidents" involving Tory candidates and representatives.
In an open letter, it tells chairman Brandon Lewis he must "ensure racists and bigots have no place" in the party.
The Muslim Council of Britain lists a series of incidents it says took place during April and at the beginning of May.
We are calling for an independent inquiry into Islamophobia in the Conservative Party following more than weekly occurrences of Islamophobia in the party last month pic.twitter.com/ymkFRDs5sF— MCB (@MuslimCouncil) May 30, 2018
Baroness Warsi, who was the first female Muslim cabinet minister as party co-chairman between 2010 and 2012, told the BBC that Theresa May or party chairman Brandon Lewis must make a "very clear statement of an acknowledgement of the issue and that the party will tackle it".
"Up to now, sadly, there are certain parts of the party that have been in denial about this issue."
She said she had been raising the issue of Islamophobia within the party for more than two years but added: "It's burying its head in the sand and now unfortunately it's playing out in a very embarrassing way, in a very public way."
Baroness Warsi said a "clear process" must be set out - be it an internal inquiry or an independent inquiry whose findings should be published and followed by a "programme of education".
She also suggested that one of the reasons the Conservatives lost ground in previous elections was because of a loss of support among Muslims and other voters from ethnic minorities.
Downing Street has defended Mrs May's approach and pointed to the prime minister's decision to establish a racial disparity audit and her appointment of Sajid Javid as the first home secretary from an ethnic minority.
In its letter, The Muslim Council of Great Britain names Harrow East MP Bob Blackman, saying he had retweeted a post on Twitter by former English Defence League leader Tommy Robinson and had hosted events in Parliament which a controversial Hindu nationalist attended.
At the time of the events, Labour and the MCB said Tapan Ghosh held "abhorrent" views about Muslims.
Mr Blackman said he did not regret sharing a platform with him, but did not agree with Tweets sent by Mr Ghosh about Muslims. Mr Ghosh has also insisted he is not Islamophobic.
In a statement on Thursday Mr Blackman said he "utterly refutes" any allegations of Islamophobia.
"I did not host Tapan Ghosh in Parliament. He was invited by an organisation without my knowledge. In the past I shared a social media post in error which I apologised for at the time. I will continue working with all communities in my constituency and I condemn Islamophobia," he said.
The letter, sent by the MCB's secretary-general Harun Khan, calls for the Tories to "publish a list of incidents of Islamophobia within the party where action has already been taken", and "adopt a programme of education and training on Islamophobia".
Lastly, Mr Khan asks that the party "reaffirm from the highest level a commitment against bigotry wherever it is found".
Responding to the letter, a Conservative spokesman said: "We take all such incidents seriously, which is why we have suspended all those who have behaved inappropriately and launched immediate investigations."