"I can't say that they will be amenable to any suggestions, but at least after I meet them I can go back and relay what they say, as just a communicator, to the leaders of the United States," he said.
The US, EU and Israel have blacklisted Hamas for its history of suicide bombings against Israel as well as its refusal to renounce violence and recognise the Jewish state.
In Washington, Tom Casey, a state department spokesman, told reporters on Monday the US had "made clear our views that we did not think now is the moment for him [Carter] or anyone to be talking with Hamas".
The US would be "happy to hear" Carter's reflections on his visit with Hamas, but it would not likely change the administration's views on the armed group, Casey said.
Carter, who was shown a house badly damaged by a rocket strike and piles of rusting projectiles collected after hitting Sderot, also offered to relay Hamas's views to Israel.
If the US 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.
Israel's senior leaders are boycotting Carter during his visit, in part because he plans to meet Khaled Meshaal, the exiled Hamas political leader in Syria.
Shimon Peres, Israel's ceremonial head of state, is the only leader who has met Carter since he arrived on Sunday.
Peres, a fellow Nobel Peace Prize laureate, criticised Carter for planning to meet Meshaal, calling it a "very big mistake", a Peres spokeswoman said.
A schedule released by Carter's aides showed no plans for talks with Ehud Olmert, Israel's prime minister, Tzipi Livni, the foreign minister or Ehud Barak, the defence minister.
The cold shoulder is a highly unusual brush-off to a former American leader - especially one so closely linked to Middle East peacemaking.
Carter brokered Israel's historic peace accord with Egypt in 1979, the first treaty it signed with an Arab country.
But his popularity has suffered in Israel after publishing a book two years ago drawing comparisons between Israeli policies in the West Bank and Gaza, and apartheid in South Africa.
The planned talks with Meshaal have fuelled Israeli discontent.
In an interview with the Israeli newspaper Haaretz, published on Monday, Carter said that he intended to use the Meshaal meeting to press for the return of three Israeli soldiers captured by Hamas and Lebanon's Hezbollah.
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 neighbours," the paper quoted Carter as saying.
"I have done everything I could in office and since I left office to do that."