Jewish organisations and politicians have expressed outrage at the decision by the new All Party Parliamentary Group on Islamophobia to retain the controversial Islamist organisation iEngage as its secretariat.

Described by the CST as having "a troubling attitude to antisemitism", concerns about its Islamist politics had earlier led to the resignation of the group's Conservative chair Kris Hopkins MP, and one of its vice-chairs, Jewish Labour peer Greville Janner.

The decision is a direct challenge to David Cameron, who called for Islamist groups to be given a wide berth in a recent keynote speech on Islamism.

The group's acting chair, LibDem president Simon Hughes, has consistently argued for keeping the link to iEngage. His position will cause embarrassment to Deputy Prime Minister Nick Clegg, who has been trying to build bridges with the Jewish community. The iEngage website claims it is "dedicated to promoting greater media awareness, political participation and civic awareness among British Muslims".

But one recent post suggested that the JC was leading a witch-hunt against Islamist Home Office adviser Asim Hafeez, who was reported to be leaving his post following Mr Cameron's Munich speech. Another suggested that far-right groups such as the English Defence League had taken comfort from the speech.

At a meeting on Monday evening, Labour's Sadiq Khan, who accused the Prime Minister of "writing propaganda for the EDL," led Labour MPs who voted to keep iEngage in place. Mr Khan is a close ally of Labour leader Ed Miliband.

Other MPs voting to keep iEngage included former Justice Secretary Jack Straw and Stephen Timms, the East Ham MP who was stabbed last year by an Islamist extremist over his support for the Iraq war.

Most Conservative MPs in the group, including Robert Halfon and Angie Bray, voted to cut links with the controversial organisation, although maverick MP Sir Peter Bottomley voted in favour.

Sir Peter, Mr Hughes and former Justice Secretary Jack Straw, who have been elected co-chairs of the APPG, have said they will investigate concerns raised about iEngage.

In a statement issued on Wednesday, they said: "Islamophobia, like antisemitism, is an unacceptable prejudice in a modern multi-faith and multi-cultural Britain. It is good that in recent years parliament has been so robust in seeking to lead public opinion in opposition to antisemitism.

"There is clearly now a parallel need to be equally robust in taking on Islamophobia. We hope that the group will soon prove itself determined and effective in taking on this role in parliament."

Mr Halfon, who has led the opposition to iEngage, said: "I am very disappointed that the committee, packed with Labour MPs, voted to kick the issue upstairs and delay banning this extremist Islamist organisation."

In what is becoming an increasingly bitter dispute, iEngage spokesperson Marjorie Thompson told the JC she did not believe Lord Janner had signed up to the APPG in good faith. "It strikes me that Greville Janner joined the group to directly sabotage it," she said.

Labour peer Lord Gulam Noon, who is a trustee of the Coexistence Trust, set up by Lord Janner and Prince Hassan of Jordan to combat antisemitism and Islamophobia, said: "Greville Janner has always fought all forms of racism, including Islamophobia"

Ms Thompson was chair of CND in the early 1990s, but is now a prominent Conservative. Her words could prove deeply embarrassing to the Prime Minister; as chair of the Conservative Cooperative Movement she is at the heart of Mr Cameron's "BIg Society" project.

Mark Gardner of the Community Security Trust said: "Islamophobia is a very important subject. The APPG should not allow itself to be compromised by the involvement of a highly politicised group such as iEngage, which also has a troubling attitude to antisemitism."

But iEngage was also facing criticism over an attack made on Mr Halfon by another website which describes him as a "nasty Israelite".

A post on the London Muslim blog, reacting to Mr Halfon's anti-iEngage stance, also denounces the former Conservative Friends of Israel political director's "virulent Israelite credentials" and describes prominent non-Jewish campaigners against antisemitism, MPs Denis MacShane and John Mann, as "the usual Israelite suspects".

Beneath the blog, a comment apparently from iEngage thanks London Muslim for its "supportive post"; the iEngage website also carries a link to the post, endorsing it as 'best of the blogs'.

Mohammad Asif, chief executive of iEngage, was unavailable for comment, but Ms Thompson said the organisation was merely thanking London Muslim for its support, not endorsing the language.

But Mr Gardner said: "The word Israelite was abused in a grotesque and hateful manner, but iEngage have endorsed it, further proving how unsuitable they are as a partner for tackling racism."

Ben Barkow, director of the Wiener Library, the research centre on Nazism and fascism, said that referring to Mr Halfon as "an Israelite" was "plainly intended to be derogatory. It superficially conflates the terms 'Jew' and 'Israeli' and implies that Jews and Israel are a single entity. Phrases such as 'nasty Israelite', 'virulent Israelite', and 'the usual Israelite suspects' leaves little doubt that this is antisemitic sloganising of a fairly crude sort."

British Fascist speakers in the 1930s and 40s sometimes used the word "Israelites" as a synonym for Jews.