Carter met senior Hamas leaders on Friday and Saturday in Syria, defying US and Israeli warnings that doing so would lend legitimacy to the group.
He is scheduled on Monday to address the Israel Council on Foreign Affairs in West Jerusalem to discuss the outcome of talks with Hamas in Syria and Egypt.
'Breaking the ice'
Al Jazeera's Mike Hanna, reporting from Damascus, said that Hamas has expressed willingness to go along with Jimmy Carter's proposals.
"However, also from the Hamas side, the point being made that something must come in return," he said.
"It will not, says Hamas, act against the interests of the Palestinian people.
"What Jimmy Carter is trying to do is to break the ice - trying to get some sort of momentum going in a situation that has been utterly static."
Hamas officials said they talked with Carter about an internationally backed Israeli embargo on Gaza and a possible Israel-Hamas prisoner swap.
Rocket fire
But Hamas did not respond to Carter's requests that it halt rocket fire on Israeli border towns and agree to talk to Eli Yishak, the Israeli deputy prime minister, about a prisoner exchange.
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The former US president put forward the following guidelines in effort start peace talks between the Palestinans and Israelis:
1. An end to hostilities, or a truce between Hamas and Israel, which includes a halt to rockets attacks.
2. Securing the release of Corporal Gilad Shalit, an Israeli soldier captured by Hamas fighters.
3. The release of Palestinians prisoners held in Israeli jails.
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Over the weekend, Israel killed seven Hamas fighters in a series of air strikes after the group detonated two jeeps packed with explosives at an Israeli crossing on the Gaza border.
Israel and the US, which both consider Hamas a terrorist group, have criticised Carter's efforts to broker negotiations.
Relations between Hamas and Jordan are frosty.
Jordan has accused Hamas of stockpiling and concealing weapons in the kingdom with the intention of using them to destabilise the pro-Western government.
Ceasefire proposed
Carter has proposed a ceasefire by Hamas and talks between the group and Yishai on an exchange of prisoners.
Muhammad Nazal, a member of Hamas' political bureau, earlier told Al Jazeera that the group would consider Carter's ideas, but "not at any price".
"This paper includes President Carter's opinion on the proposed cases," he said.
"Regarding the calm issue [of a ceasefire], President Carter calls for a goodwill stance and initiative by Hamas movement to 'embarrass' the Israelis."
Nazal said that Carter's proposals also examined conditions for the possible release of Gilad Shalit, an Israeli soldier who was captured by Palestinian fighters in June 2006.
Detailed viewpoint
"The other issues include a prisoner exchange and Gilad Shalit ... there is a detailed viewpoint that I do not want to tackle now," Nazal said.
"There is also a vision towards lifting the blockade imposed on the Gaza Strip, and others related to the Rafah [border] crossing [between Gaza and Egypt]."
Hamas, which has overall control of the Gaza Strip after routing Fatah forces there in July 2007, may allow Fatah-allied guards to stand at the Rafah crossing, Mahmoud Zahar, a senior Hamas official, said.
However, Nazal said Hamas agreed to study Carter's proposals "only as part of a number of prices that will achieve public interest for the Palestinian people".