The peace camp is encouraged by recent developments
The group, the Council for Peace and Security, also wants a resumption of peace talks with the Palestinians and the immediate establishment of a Palestinian state - whether violence continues from the Palestinian side or not.
One member told the BBC that Israeli Prime Minister Ariel Sharon's determination to crush the Palestinian intifada, or uprising, by military means was fuelling further Palestinian attacks.
Israeli press reports say about 80% of the Council for Peace and Security's membership has signed up to the proposals, believing they will force the Palestinian leadership to renew its commitment to providing security to the Israeli population.
Saying 'shalom'
The group is now launching a campaign, which will include public appearances, bumper stickers and a pamphlet entitled "Saying shalom to the Palestinians" - shalom meaning both peace and farewell.
The campaign comes on the heels of a new campaign by Israel's peace movement, under the slogan "Get out of the territories, get back to being ourselves".
A peace rally in Tel Aviv on Saturday drew thousands of demonstrators.
BBC correspondent Caroline Hawley says the campaign is part of mounting criticism of Ariel Sharon's hardline policy towards the conflict with the Palestinians.
And, with no political or military solution in sight, the strong support he has enjoyed until now seems to be eroding, our correspondent says.
Israelis are still deeply disillusioned with Yasser Arafat, but the Israeli left, which has been dormant for the past year and a half, appears now to be coming back to life.
A protest by reservist officers and soldiers who refuse to serve in the occupied territories, is now growing steadily.
Reservist rebellion
More than 250 reservists have signed a petition saying they will not take part in what they call missions of oppression.
Reserve major general Danny Rothschild, who is president of the Council for Peace and Security, said dissatisfaction among reservists was the deciding factor for him in backing the campaign.
"Four months ago it was clear to me that the movement would grow if we continue calling up reserves to accompany settlers to music lessons and to protect real estate that has nothing to do with ideology," he said in comments published in the Israeli newspaper Haaretz.
He said the Council's plan to evacuate some 40-50 settlements in the West Bank, where only about 15% of settlers live, would free up troops to guard the pre-1967 armistice lines.
Israel seized the West Bank and Gaza during the 1967 Six Day War, establishing hundreds of settlements in the territories that are regarded as illegal by international law.
Israeli forces withdrew by stages from many Palestinian towns and villages during the Oslo peace process in the 1990s, while the fate of settlements on occupied land was left to be determined in failed final status negotiations.