Carter, speaking in Jerusalem earlier on Monday, said that Hamas had told him it would accept the right of Israel "to live as a neighbour" if a peace deal was approved by a Palestinian referendum.
Carter said Hamas leaders had told him they would "accept a Palestinian state on the 1967 borders if approved by Palestinians".
But Carter also said Meshaal turned down his appeal for a unilateral ceasefire with Israel to end violence threatening peace efforts.
"I did the best I could on that," Carter said of his failure to persuade Hamas to halt rocket fire for one month from the Gaza Strip it has controlled since June when it ousted the Fatah movement of Mahmoud Abbas, the Palestinian president.
US dismisses comments
The United States brushed off Carter's report on Hamas on Monday, saying the group's basic stance had not changed.
"What is clear to us ... is that nothing has changed in terms of Hamas's basic views about Israel and about peace in the region," Tom Casey, the state department spokesman, said.
"They still refuse to acknowledge or recognise any of the basic quartet principles, including recognising Israel's right to exist; renouncing terrorism; and acknowledging all the previous agreements that have been made between the Palestinian Authority and Israel," he added.
Dana Perino, the White House press secretary, said the Hamas position should be taken "with a grain of salt".
"We have to look at the public comments and we also have to look at actions, and actions speak louder than words."
Carter said his understandings with Hamas called for a referendum to be preceded by reconciliation between the group and Abbas's Fatah faction.
In his news conference, Meshaal said Hamas would "respect Palestinian national will, even if it was against our convictions".
Sami Abu Zuhri, a Gaza-based Hamas official, said Palestinian refugees living in exile must take part in a referendum - a condition that could dim the chances of approval since Israel opposes their mass return, which could skew the state's ethnic make up.
Ghazi Hamad, a former Palestinian government spokesman, told Al Jazeera that Hamas would be willing to accept a Palestinian state within the 1967 borders (leaving a reduced Israeli state inside its 1948 borders) but insisted that Hamas would not recognise Israel.
|Carter, in his news conference, said excluding|
Hamas was 'just not working'
"Hamas says frankly - we will not recognise the right of Israel," he said.
"Israel until now has no clear position on recognising the rights of the Palestinian people within the 1967 borders or the right of return or the rights in Jerusalem."
He also said that a ceasefire with Israel was possible.
"Many times Hamas has stopped firing missiles from Gaza but Israel continues its aggression against our people, especially in Gaza," he told Al Jazeera.
"If Israel stops all military aggression against our people, I think Hamas will have no problem in reaching a compromise."
Carter's meeting with Hamas has drawn criticism from both the Israeli and US administrations.
Ehud Olmert, the Israeli prime minister, has refused to see Carter, who has for years been critical of Israeli policy towards the Palestinians.
Carter, who helped negotiate a 1979 peace treaty between Israel and Egypt, said excluding Hamas is "just not working".
"The problem is that Israel and the United States refuse to meet with these people, who must be involved," he said.