"I think it is absolutely crucial that in the final and dreamed-about and prayed-for peace agreement for this region that Hamas be involved and Syria will be involved," he told a business conference outside Tel Aviv.
"I can't say that they will be amenable to any suggestions, but at least after I meet with them I can go back and relay what they say, as just a communicator, to the leaders of the United States," he said.
The U.S., EU and Israel have blacklisted Hamas for its history of killing some 250 Israelis with suicide bomber attacks and its refusal to renounce violence and recognize the Jewish state.
Israel's top leaders are boycotting Carter during his nine-day Mideast trip, in part because he plans to meet later in the week in Syria with Hamas' exiled supreme leader, Khaled Mashaal.
In Washington, State Department spokesman Tom Casey said the U.S. government has "made clear our views that we did not think now is the moment for him or anyone to be talking with Hamas."
U.S. officials will be "happy to hear" Carter's reflections on his visit with Hamas, but that they aren't likely to change the administration's views on the militant group, Casey said.
The Democratic chairman of the House Foreign Relations Committee criticized Carter for meeting with Hamas. Carter "in effect is undermining a current policy which is not just American but held by many others," Rep. Howard Berman of California told The Associated Press.
Carter also offered to relay Hamas' views to Israel. If the U.S. agrees to hear what Hamas says, "I hope then the Israeli government will deign to meet with me -- they have so far refused," he said.
President Shimon Peres, Israel's ceremonial head of state, was the only leader to meet with Carter since he arrived Sunday. Peres, a fellow Nobel Peace Prize laureate, criticized Carter for planning to meet with Mashaal, calling it a "very big mistake," a Peres spokeswoman said.
A schedule released by Carter's aides showed no plans for talks with Israeli Prime Minister Ehud Olmert, Foreign Minister Tzipi Livni or Defense Minister Ehud Barak.
The cold shoulder is a highly unusual brush-off to a former U.S. leader -- especially one so closely linked to Mideast peacemaking.
Carter brokered Israel's historic peace accord with Egypt in 1979, the first treaty it signed with an Arab country. But his popularity fell in Israel after he published a book two years ago drawing comparisons between Israeli policies in Palestinian areas and apartheid in South Africa. The planned talks with Mashaal only fueled Israeli anger.
In an interview published Monday in the Israeli newspaper Haaretz, Carter said he intended to use his meeting with Mashaal to press for return of three Israeli soldiers captured by Hamas and the Lebanese Hezbollah militia. He said he would also try to get Hamas to accept an Arab plan for peace with Israel.
"The most important single foreign policy goal in my life has been to bring peace to Israel, and peace and justice to Israel's neighbors. I have done everything I could in office and since I left office to do that," the paper quoted Carter as saying.
On Monday, Carter toured Sderot, the southern Israeli town targeted most frequently by Palestinian rocket squads in the Gaza Strip. He was shown a house badly damaged by a rocket strike and piles of rusting projectiles collected after hitting the town. More than 1,000 rockets have exploded in Sderot in the past year.
"I think it's a despicable crime for any deliberate effort to be made to kill innocent civilians, and my hope is there will be a cease-fire soon," Carter told reporters.