Former U.S. President Jimmy Carter met Hamas Prime Minister Ismail Haniyeh in Gaza City on Tuesday during his visit to Israel and the Palestinian territories.
Carter stressed the importance of the proposals laid out by U.S. President Barack Obama in his recent speech in Cairo, saying that there should be two "sovereign nations" living side by side, with a "right to exist and to live in peace."
Hamas Prime Minister Ismail Haniyeh said he would welcome a "real project" to establish a Palestinian state according to the borders of Palestinian territory before the 1967 Six Day War.
Carter said he was trying to persuade Hamas leaders to accept the international community's conditions for ending its boycott of the Islamic militant group.
The international community has asked Hamas to recognise Israel, renounce violence and accept previous peace deals.
Hamas has said such concessions cannot be made up front.
Carter was also expected to deliver a note to Haniyeh from the parents of Israeli soldier Gilad Schalit, who was captured by Hamas militants in 2006 and remains in captivity in the Gaza Strip.
Haniyeh said Carter had discussed Schalit with a delegation representing Hamas leaders, and that Hamas would encourage dialogue to reach an "honoured" prisoner-exchange deal.
Carter said he planned to meet with officials in the Obama administration after his talks in Gaza.
The former U.S. president met with Hamas' exiled leadership in Syria on Thursday and said they wanted "peace and they want to have reconciliation, not only with Fatah brothers but also eventually with the Israelis."
Hamas is being shunned by most of the international community, including the U.S., for refusing to recognise Israel or renounce violence, though Hamas leader Khaled Mashaal has said repeatedly in recent weeks that his group wants to be part of a Middle East solution.
Earlier Carter visited sites damaged during Israel's onslaught on the Gaza strip, including an American school.
Israel launched its punishing offensive against Gaza's Hamas rulers and the Gazan people on 27 December, it says, to try to halt eight years of rocket fire into its southern territory and deal a heavy blow to the Hamas militant group.
The operation killed more than 1,400 Palestinians, including more than 900 civilians, amongst them scores of children, according to Palestinian officials and human rights groups.
It also destroyed thousands of homes and heavily damaged Gaza's infrastructure.
Israel claims the death toll was lower and most of the dead were Hamas militants.
It blames Hamas for the civilian casualties, saying the militants used schools, mosques and residential areas for cover, a claim Hamas denies.
Thirteen Israelis were also killed during the fighting.
A strict Israeli and Egyptian blockade, the latter on one border, of the impoverished and battered coastal strip has meant desperately needed materials to rebuild have not been allowed through.
