The Labour MP has already stood down from her position as aide to the Shadow Chancellor John McDonnell this morning, however critics say she must now resign from the influential Commons committee and should also be suspended from the party.
The Conservative Group on Bradford Council said her anti-Israel backing is incompatible with its current examination of the rise of anti-Semitism.
Councillor Simon Cooke, Leader of the Conservative Group said: “I have written to the Leader of the Labour Party, Jeremy Corbyn MP, asking for Naz Shah MP to be suspended from the Party while a full investigation is conducted into her apparent support for anti-Semitic ideas such as the forced transportation of Jews from Israel. I’m also asking for Ms Shah to be removed from the Home Office investigation into anti-Semitism in the UK.
“Anti-Semitism cannot be tolerated and I hope that the Labour Party treats Naz Shah MP in the same way as Labour councillors and members who have posted offensive, anti-Semitic material on social media – through suspension and a full investigation.”
He said without an investigation into Ms Shah, the people of Bradford are likely to be unable shake the thought that one of the district’s MPs is far from committed to community cohesion.
In a Facebook post in 2014, before she became an MP, Ms Shah shared a graphic which showed an image of Israel’s outline superimposed onto a map of the US under the headline “Solution for Israel-Palestine Conflict - Relocate Israel into United States”, with the comment “problem solved”.
The post suggested the US has “plenty of land” to accommodate Israel as a 51st state, allowing Palestinians to “get their life and their land back”.
It added that Israeli people would be welcome and safe in the US while the “transportation cost” would be less than three years’ worth of Washington’s support for Israeli defence spending.
Ms Shah, who was elected at the General Election in 2015 beating Respect politician George Galloway, added a note suggesting the plan might “save them some pocket money”.
After the posting was highlighted by the Guido Fawkes website, the 42-year-old released a statement in which she said: “This post from two years ago was made before I was an MP, does not reflect my views and I apologise for any offence it has caused.”
She then wrote on Twitter: “I am truly sorry and I will be putting out a more detailed explanation later.”
She added that she “deeply regretted” the hurt caused by her comments and accepted there was “no excuse” for the offence they caused.
However campaigners against anti-Semitism continued to raise concerns, with one group saying it would be “hard” for them to take seriously an inquiry into anti-Semitism being conducted by the House of Commons Home Affairs Committee so long as she remained a member.
In a second statement, Ms Shah announced she was standing down from her unpaid role as Mr McDonnell’s parliamentary private secretary.
“I deeply regret the hurt I have caused by comments made on social media before I was elected as an MP,” she said.
“I made these posts at the height of the Gaza conflict in 2014, when emotions were running high around the Middle East conflict. But that is no excuse for the offence I have given, for which I unreservedly apologise.
“In recognition of that offence, I have stepped down from my role as PPS to the shadow chancellor John McDonnell.
“I will be seeking to expand my existing engagement and dialogue with Jewish community organisations and will be stepping up my efforts to combat all forms of racism, including anti-Semitism.”
Speaking before Ms Shah’s second statement, Jonathan Sacerdoti, director of communications at the Campaign Against Antisemitism, said: “One cannot simply apologise for ‘any offence caused’ and expect evidence of gross and brazen anti-Semitism to disappear.
He added: “We have offered to assist the select committee in its work investigating anti-Semitism. However, if Naz Shah remains on the committee it will be hard for those of us giving evidence to take the inquiry seriously.”
The comments come a week after she wrote to the Prime Minister David Cameron to outline her concerns amid allegations of anti-Semitism, discrimination, misogyny, and clan politics surrounding the deputy chairman of the Bradford Conservative Association, Abdul Zaman.
Mr Zaman was accused of making the comments during a speech to start Tory candidate Sajid Akhtar’s campaign for election to Bradford Council in the Heaton ward.
He has since been suspended from the party pending an investigation into the incident.
Bradford Conservative group leader Simon Cooke said: “I find it breathtakingly hypocritical of Naz Shah to write to the Prime Minister raising concerns about anti-Semitic language from Abdul Zaman, a Conservative campaigner in Ms Shah’s Bradford West Constituency having previously supported calls for the forced transportation of Jews from Israel to America.”