"The key thing is for Israel to give up its ambition to occupy and control Palestine," Mr. Carter said on CBS' "The Early Show."
"As long as they are still building Israeli homes in Palestine, against the wishes of the Palestinian people, that makes it very difficult for the Palestinians or the Arab world to comply with the desires of the United States, and that is to have peace.
"But it's always better, when you look at the Middle East, to have some hope," Mr. Carter said.
He also spoke approvingly of Secretary of State Hillary Rodham Clinton, saying there is no better mediator.
"I don't think we could have any better interlocutor or mediator than Hillary Clinton, who is tough, competent, knowledgeable, intelligent and I think very determined to be successful," President Carter told anchor Harry Smith. "So, if anybody can do it, I think Hillary Clinton can do it."
The Palestinians had warned they would walk away from talks if the Israelis' moratorium on settlement building was not extended.
Despite entreaties by White House envoy George Mitchell and other governments, Prime Minister Benjamin Netanyahu has refused to continue the ban, due to pressure from his government's pro-settlement coalition. But he has asked the Palestinians to continue with the peace process even after building has resumed.
Tensions have increased in the West Bank, as arsonists set fire to a mosque in a Palestinian village on Monday, and wrote "revenge" in Hebrew on a wall. Hardline Jewish settlers are suspected in the blaze.
"Is there any compelling argument that could be made to the Palestinians to continue on?" Smith asked Carter.
"Well, I think if there's an assurance that Israel will get out of Palestine and let the Palestinians have their own viable and contiguous nation, fine," said Mr. Carter. "But in addition to building the homes, Israel is insisting that they still remain occupying the Jordan River valley and controlling Palestine from air and ocean and land, so that the Palestinians don't have any access to the outside world.
"This is a major obstacle to overcome, and I hope that there will be some flexibility on both sides to let the United States mediation prevail."