Carter has proposed a ceasefire by Hamas and talks between the group and Eli Yishai, Israel's deputy prime minister, on an exchange of prisoners.
Muhammad Nazal, a member of Hamas' political bureau, told Al Jazeera that the group will consider Carter's ideas, but "not at any price".
"This paper includes president Carter’s opinion towards 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," he said.
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.
"The other issues include a prisoner exchange and Gilad Shalit ... there is a detailed viewpoint that I do not want to tackle now," he 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".
He said Hamas leaders based in the Gaza Strip would hold their own talks with Meshaal before giving Carter a response to his plans.
Carter's landmark meeting with Meshaal in the Syrian capital Damascus drew staunch criticism from Israel and the US administration.
During Carter's visit to Israel earlier this week, Ehud Olmert, the country's prime minister, refused to meet the former US president over his plan to meet with Hamas leaders.
Sean McCormack, US state department spokesman, said on Friday that Carter had opened himself up to "exploitation" by Hamas.
"We find it very odd that one would encourage to have a conversation between the Israeli government and Hamas, which doesn't even recognise the right of the Israeli government to exist," McCormack said.
While Israel is involved in a peace dialogue with Fatah, led by Palestinian prime minister Mahmoud Abbas, Hamas is not a party to the talks, primarily because it does not recognise Israel.
Out of the diplomatic "quartet" of entities involved in mediating the Israeli-Palestinian peace process - the US, the EU, the UN and Russia - only Moscow does not list Hamas as a terrorist organisation.
Source: Al Jazeera and agencies