"It comes from the European Jewish communities who are profoundly attached to Israel and who want to say that current Israeli policies are both a source of anxiety for us and a source of insecurity in the long term for Israel as well as a source of injustice for the Palestinians," Patrick Krugman, a French lawyer and spokesman for the group, said.
The document calls on the EU and the US to pressure both parties "and help them achieve a reasonable and rapid solution to the Israeli-Palestine conflict."
It says that systematic support of Israeli government policy is dangerous.
The petition's signatories include Bernard-Henri Levy and Alain Finkielkraut, French philosophers, as well as Daniel Cohn-Bendit, leader of the student protests in the 1960s and a politician in the European parliament.
"These are people who seize every opportunity to defend Israel publicly and remain faithful to it," Yossi Sarid, an ex-Knesset member, said of the key figures of JCall.
"Even during Operation Cast Lead and after the Goldstone report they were on Israel's side. The State of Israel is the apple of their eye in good times, and especially in bad."
Yael Kahn, an Israeli Jew, told Al Jazeera, that as someone campaigning against the Israeli abuse of Palestinian human rights, she was pleased to hear that JCall was openly criticising Israeli policies.
"However, I find the "Call for reason" wholly inappropriate, due to its failure to mention the fact that these settlements are illegal," Kahn, chair of a UK-based activist group, Islington Friends of Yibna, said.
"I am utterly appalled by the failure of the petition to mention Gaza and the barbaric siege Israel imposes on the 1.5 million Palestinians living there," she said.
"It is outrageous to not speak out against the Israeli restrictions on the amount of food Palestinians in Gaza are allowed to have."
She said that she was in regular contact with the victims of the Israeli policy of deprivation and called "on every person of conscience to take action to lift the siege imposed by Israel".
Similar to JStreet
JCall hope to build a European movement that is both "committed to the state of Israel and critical of the current choices of its government."
This initiative comes amidst increasing criticism of Israeli policies from Jewish groups both within Israel and in the US and Europe.
JCall say that they are based on the same principles as JStreet, a group of American Jews which recently came together in the US.
Israel's Foreign Ministry declined to comment because the initiative is not government sponsored.
Many signatories are from France, where the petition has received much press coverage.
However, the president of CRIF, France's leading Jewish association, declined to sign, saying he objected to some of its language and its tone.
"I think our initiative is actually helping Israel's image in Europe," Chemla said, responding to a claim that putting pressure on Israel was irresponsible.
"It is a pretty low image over here these days, because of what happened in Gaza, mainly, and it is commonly believed in Europe that Israel is the provocative, negative side of the conflict - the one that is blocking the peace process."