The Muslim Council of Britain has accused the Conservative Party of “denial, dismissal and deceit” over the issue of Islamophobia.
The MCB said the party had a “blind spot for this type of racism” and had failed to take steps to tackle it.
The group was responding to criticism of Labour’s handling of anti-Semitism by the chief rabbi.
Conservative leader Boris Johnson said party members guilty of Islamophobia “are out first bounce”.
In the Times, Chief Rabbi Ephraim Mirvis said Labour had not done enough to tackle anti-Semitism and urged people to “vote with their conscience” in the general election.
He wrote that the “overwhelming majority of British Jews are gripped by anxiety” at the prospect of a Labour victory in the 12 December poll.
In response, the MCB said British Muslims would “listen to the chief rabbi and agree on the importance of voting with their conscience”.
A spokesperson added that the “unacceptable presence of anti-Semitism in Britain” was a source of “real fear” for British Jews.
They added the chief rabbi’s comments “highlighted the importance of speaking out on the racism we face, whilst maintaining our non-partisan stance.”
“It is abundantly clear to many Muslims that the Conservative Party tolerate Islamophobia, allow it to fester in society”.
The spokesperson added that the issue was “particularly acute” within the party itself.
‘Letter boxes’ controversy
The MCB is an umbrella organisation of various UK Muslim bodies, including mosques, schools, and charitable associations.
It has previously called for allegations of Islamophobia in the Conservative Party to be investigated by the Equalities and Human Rights Commission – the body which is currently investigating allegations of anti-Semitism in the Labour Party.
Speaking to reporters, Mr Johnson said: “If anybody is convicted, if anybody is done for Islamophobia, or any other prejudice or discrimination in the Conservative Party they are out first bounce.”
But Mr Johnson has also faced accusations of Islamophobia himself, after he wrote in a newspaper column last year that Muslim women wearing burkas “look like letter boxes”.
Also speaking on Tuesday, Chancellor Sajid Javid refused to criticise the prime minister for these remarks, added he had “explained why he’s used that language”.
He said the column from which the quote was taken had defended the rights of Muslim women to “wear what they like”, adding: “He’s explained that, and I think he’s given a perfectly valid explanation.”
The Conservatives have pledged to start an investigation into Islamophobia and other forms of prejudice within the party before the end of the year.
The party suspended a number of members earlier this month after the Guardian supplied it with a dossier produced by an anonymous Twitter user containing examples of allegedly Islamophobic social media posts.
A number of members were also suspended in September, after the BBC highlighted 20 cases to the party of members posting or endorsing Islamophobic material online.