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It is understood the move followed approaches first from an organisation UK Lawyers for Israel and then by the Israeli authorities.
When the meeting began today a council official told councillors the item had been withdrawn from the committee agenda to allow officers to “give full consideration to legal matters raised since publication of the agenda”.
Campaigner Pete Gregson, who submitted the petition, said he had been told of the withdrawal at 5pm yesterday, just 17 hours before the meeting.
And he quoted council leader Adam McVey as saying: "The Israeli authorities have challenged any consideration of the matter, even to negatively consider, as unlawful, on grounds it “could” support Hamas, a listed terrorist organisation. It’s ridiculous conjecture.”
Mr Gregson said: “The Israeli intervention was prompted by the UK Lawyers for Israel threat of last Thursday which warned councillors that if they went ahead and twinned, they could be facing 14 years in prison.
“Israel is undermining our democracy with threats, stopping friendly relations between cities.”
And he said the city of Gaza was not run by Hamas
"Whilst Hamas are in overall control of the whole Gaza Strip, the various municipalities and refugee camps basically run their own affairs, in the same way as we do in Scotland. But they have a very different means of appointing their local councillors. In the UK we only adopted a party mechanism in local authority elections since around 1920; prior to then, folk were elected on their individual merits. In the same way in Gaza, the party system is not used; individuals, rather than parties control the municipality.”
Last week, Mr Gregson told the Evening News that twinning with Gaza would be a fundamentally humanitarian act because the city had been under siege for 15 years.
Gaza City has a population of around 550,000, roughly similar to Edinburgh’s 450,000. Dundee is already twinned with Nablus and Glasgow with Bethlehem.
Mr Gregson’s petition attracted 326 signatures, comfortably passing the 200 threshold required for it to be considered by councillors, and the twining proposal was also supported by 115 people in Gaza who signed a sister petition addressed to Edinburgh council leaders.
A council spokesperson said: “The report considering the petition was withdrawn so the committee could receive legal advice on specific points that were raised. Once legal advice is received Councillors will then be able to consider a response to the petition, based on Edinburgh’s current international framework.”