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.
Tory MP James Brokenshire said his party had robust procedures against anti-Muslim hatred.
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 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 on BBC Politics Live, Mr Brokenshire – a former communities secretary and Tory parliamentary candidate – said his party took Islamophobia claims “incredibly seriously”.
“We want to ensure that the Conservative Party has robust procedures. We think that we do,” he said.
“But we want to check that, we want to determine that, which is why we are committed to this independent review by the end of this year.”