Sari Nussaibah, the president of Al-Quds University and Ami Ayalon, the former head of Israel's domestic security agency, outlined their own peace plan to the UN secretary general on Wednesday.
Scorned by Israeli Prime Minister, Ariel Sharon, the two campaigners have gathered supporting signatures of 100,000 Israelis and 60,000 Palestinians in a three-month period.
Their plan, "The People's Voice", is similar to what ex-President Bill Clinton proposed three years ago and Yasir Arafat rejected. Since then, Sharon has done the same.
A Palestinian state would be created in the West Bank and Gaza, minus some border modifications on land adjacent to Israel where many Jewish settlers live.
Jerusalem would be divided according to its already segregated neighbourhoods and become the capital of both nations.
"This speaks honestly to people, presenting them with the principles that will be the basis for any viable two-state solution"
And in exchange for Israel removing Jewish settlements in the occupied territories, the Palestinians would forgo the "right of return" for four million refugees and their descendants. The Palestinian state would then be demilitarised.
Nussaibah, a Palestine Liberation Organisation veteran, said their proposals needed to be inserted into the "road map", drawn up by the United States, Russia, the European Union and the United Nations.
"This one page insert outlines the vision that is absent in road map," he said. "This speaks honestly to people, presenting them with the principles that will be the basis for any viable two-state solution."
Israel's Ayalon said after the meeting with Annan that time is running out for the two-state solution.
He said: "Time is against the option of a two-state solution, which is the only way for Israel to have a safe home and the Palestinians to have a state."
He added that demographic considerations and Israeli settlements were altering the situation and that people were slowly giving up hope.
"More and more people do not believe any more that we can have it."
"Time is against the option of a two-state solution, which is the only way for Israel to have a safe home and the Palestinians to have a state"
Former head of Israeli security agency
Annan applauded their efforts and courage, saying that grass-roots initiatives "helped to create a vision of a common future".
Dormant road map
While there was no substitute for official negotiations, Annan said "people-to-people initiatives can play an essential role in generating the momentum needed for peace".
The nearly dormant road map lays out steps the two sides should take along the way to setting up a Palestinian state by 2005.
But it has been bogged down over Israeli demands that the Palestinian Authority should crack down on resistance fighters and Palestinian suspicions that Israel would give nothing in return.
Among the main sticking points of the road map are the status of Jerusalem, the right of return of Palestinian refugees and Jewish settlements in the occupied territories.