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”.
“This an issue that is particularly acute in the Conservative Party.”
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 UK’s human rights watchdog is currently investigating allegations of anti-Semitism in the Labour Party.
The Conservatives have pledged to start an investigation into Islamophobia and other forms of prejudice within the party before the end of the year.
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.”
Earlier, Chancellor Sajid Javid told the BBC: “What we have done is changed laws, we’ve increased penalties, we’ve encouraged reporting.
“That’s important to make sure that the whole country, the police and all institutions, are working really hard to root out hatred,” he said.