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A government spokesman also said Israel was unimpressed by Meshaal's statement.
"Israel is targeted on a daily basis by rocket barrages from Hamas controlled territory in the Gaza Strip. Israel sees no change in Hamas's extremist positions," said David Baker, a spokesman in Prime Minister Ehud Olmert's office.
In Washington, the U.S. State Department said there is no indication that Hamas wants peace with Israel. "It is pretty clear to us that there is no acceptance on the part of Hamas of any kind of negotiated settlement," said deputy spokesman Tom Casey.
Casey said there had been contradictory statements from Hamas officials over whether they would accept the result of a referendum on a peace deal.
Earlier in Jerusalem, Carter said that Hamas is prepared to accept the Israel's right to "live in peace" within 1967 borders.
"There's no doubt that both the Arab world and the Palestinians, including Hamas, will accept Israel's right to live in peace within the 1967 borders."
Hamas has previously claimed all of what is now Israel and the West Bank and Gaza, and its charter calls for the destruction of Israel. Meshal did not address whether the group would consider changing it. But his comments were one of the strongest Hamas statements in favor of a two-state solution.
"This is Hamas' clear vision," Meshal added. He said the future Palestinian state must have Jerusalem as its genuine, sovereign capital. He appeared to be referring to East Jerusalem, since Israel held west Jerusalem before 1967.
Carter's comments came after he met after he met last week with the top Hamas leaders, including Meshal, in Syria.
Carter was back in Jerusalem this week to brief Israeli leaders on his talks with Meshal regarding a proposed truce between Israel and Hamas in the Gaza Strip as well as an exchange of prisoners between them.
Carter: Hamas would accept Israel-PA deal if Palestinians vote for it
The former U.S. president told reporters in Jerusalem on Monday that Hamas leaders said they would accept a peace agreement negotiated by their rival, Palestinian President Mahmoud Abbas, if Palestinians approved the deal in a vote.
"They said they would accept a Palestinian state on the 1967 borders if approved by Palestinians ... even though Hamas might disagree with some terms of the agreement," Carter said in a speech, after talks in Syria and Egypt with Hamas leaders.
"It means that Hamas will not undermine Abbas' efforts to negotiate an agreement and Hamas will accept an agreement if the Palestinians support it in a free vote," he said.
But Carter said he was told by Hamas that a referendum on a peace deal must be preceded by reconciliation between the group and Abbas' Fatah faction. Hamas seized the Gaza Strip from Fatah in fighting in June.
A Hamas official in the Gaza Strip also referred to a series of preconditions raised by the Islamist group for assenting to a deal with Israel.
Sami Abu Zuhri said Palestinian refugees living in exile must be included in the voting - a condition that could complicate approval of a deal.
Abu Zuhri also noted that Hamas, which refuses to recognize Israel, would regard any future Palestinian state in the West Bank and the Gaza Strip, territories Israel captured in the 1967 Six Day War, as "transitional".
Speaking later to reporters, Carter said Hamas leaders whom he met "didn't say anything about transitional".
Unlike Abbas, who sought a Palestinian state side-by-side with Israel, Abu Zuhri said Hamas's outstanding position not to recognize Israel's right to exist remained unchanged despite of its acceptance of a state in 1967 borders.
Carter said Hamas turned down his proposal for a 30-day unilateral cease-fire with Israel but Egypt would continue its efforts to mediate a truce.
"I did the best I could on that," Carter said of his failure to persuade Hamas to halt rocket fire from the Gaza Strip.
Carter: Hamas ready to release letter from Shalit
Carter also told Trade Minister Eli Yishai on Monday that Hamas was prepared to release another letter from abducted Israel Defense Forces soldier Gilad Shalit to his family.
According to Carter, Meshal has promised that Shalit - who was kidnapped by Hamas militants in a cross-border raid in June 2006 - is in good physical health.
Carter told Yishai that Hamas was prepared to transfer Shalit into Egyptian hands as part of a packaged deal which would include the release of Palestinian prisoners.
The former U.S. leader said the Islamists had no opposition to releasing the soldier as part of a prisoner swap. He also asked Yishai to consider meeting with officials in Egypt regarding Shalit's release.
Yishai responded that he has already met with Egyptian President Hosni Mubarak and the Egyptian intelligence chief, Omar Suleiman, on the matter, but said he would consider another meeting.
The former U.S. leader told Yishai that Meshal had appreciated Yishai's offer to meet with the Islamist group regarding the Shalit deal, but did not want to compromise Egyptian mediation by doing so.
'Problem is refusal of U.S., Israel to meet Hamas'
Carter also told reporters following his return to Israel on Monday the "problem" was not his decision to meet with the Islamist group, but rather the refusal of Israel and the U.S. to do the same.
"The problem is not that I met with with Hamas in Syria. The problem is that Israel and the United States refuse to meet with someone who must be involved," the former U.S. leader said during a speech in Jerusalem.
He urged Israel to engage in direct negotiations with Hamas, saying failure to do so was hampering peace efforts.
"We do not believe that peace is likely and certainly that peace is not sustainable unless a way is found to bring Hamas into the discussions in some way," he said. "The present strategy of excluding Hamas and excluding Syria is just not working."
In his comments Monday, Carter said Israeli-Palestinian peacemaking has regressed since a U.S.-hosted Middle East conference in Annapolis, Maryland, in November.
Speaking about the possibility of renewed peace talks between Israel and Syria, he said Syria wants the U.S. to play a strong role in bringing to two sides together.
Both the Israeli and U.S. governments disapprove of Carter's overtures to Hamas. Over the weekend, Prime Minister Ehud Olmert said he decided not to meet with Carter in Israel because he does not wish to be seen as participating in any negotiations with Hamas.