A new European group modelling itself on J Street, the left-leaning American Israel lobby, was launched at the European Parliament on Monday.
Hundreds of supporters of J Call, including MEPS and two former Israeli envoys, presented a petition asking Israel to stop its settlement activity and calling on Europe to intervene.
Headed "a European Jewish Call for Reason" and partially written by former Israeli envoy to France Elie Barnavi, the online petition has been signed by more than 4,700 people.
It asks the EU to put pressure on Israel and the Palestinians to make "the necessary moves to establish peace" and calls on Israel to stop building in the West Bank and in "the Arab districts of east Jerusalem". Leaders say they will also demand that Palestinians renounce the right of return.
"Some say our initiative hurts Israel, but it's the exact opposite: we aim to save Israel from disaster," said founder David Chemla, head of the French branch of Peace Now. "Israel cannot remain a democratic Jewish state if it keeps occupying the West Bank."
But he was unable to explain what kind of measures it wants the EU to take against Israel, adding: "We're obviously pro-Israeli and are opposed to any kind of boycott."
While MEP Daniel Cohn-Bendit told the crowd, to loud applause, that "the Zionist dream is not my dream", others, including philosophers Bernard Henri Levy and Alain Finkielkraut, are known for their unwavering support for Israel. Their involvement triggered a backlash from French umbrella group CRIF, whose leader Richard Prasquier accused J Call of endangering Israel and helping its enemies.
An online counter-petition gathered more signatures than the original. But Mr Levy brushed the accusations aside.
"Debate and differences of opinion make us stronger, not weaker. It's absurd to think Zionists shouldn't express themselves," he said.
And several signatories, including Mr Barnavi, disagreed that an impartial call was necessary.
"It's a call from diaspora Jews to Israel. It would be ridiculous to balance every single statement," he said.
Signatories also rejected claims that they were attempting to override the will of Israeli voters, with former ambassador to Germany Avi Primor arguing that J Call does not stop the Israeli government from implementing its policies.
It remains unclear whether such an appeal can get significant support in Europe and whether J Call - currently only a petition - can be transformed into an effective political tool.
There is at least one British signatory - Engage's David Hirsch - but sources say that British groups which were approached declined to join until it was clear whether J Call was well received and its goals were clarified. Mr Chemla is visiting London next week to meet potential signatories.