Apart from the time restriction and the refusal to accept Israel’s existence, Mr. Meshal’s terms approximate the Arab League peace plan and what the Palestinian Authority of President Mahmoud Abbas says it is seeking. Israel rejects a full return to the 1967 borders, as well as a Palestinian right of return to Israel itself.

Image Khaled Meshaal, the political leader-in-exile of Hamas, in Damascus. Credit... Mumtaz al-Baloua for The New York Times

Regarding recognition of Israel, Mr. Meshal said the Palestinian leader Yasir Arafat and Mr. Abbas had granted such recognition, but to no avail. “Did that recognition lead to an end of the occupation? It’s just a pretext by the United States and Israel to escape dealing with the real issue and to throw the ball into the Arab and Palestinian court,” he said.

In April, only six rockets and mortar rounds were fired at Israel from Gaza, which is run by Hamas, a marked change from the previous three months, when dozens were shot, according to the Israeli military. In late December, Israel began a three-week invasion of Gaza, saying that it sought to stop the rockets, which land on its southern communities. About 1,300 Palestinians were killed in the invasion.

Mr. Meshal made an effort to show that Hamas was in control of its militants as well as those of other groups, saying: “Not firing the rockets currently is part of an evaluation from the movement which serves the Palestinians’ interest. After all, the firing is a method, not a goal. Resistance is a legitimate right, but practicing such a right comes under an evaluation by the movement’s leaders.”

He said his group was eager for a cease-fire with Israel and for a deal that would return an Israeli soldier it is holding captive, Cpl. Gilad Shalit, in exchange for many Palestinian prisoners.

Iran is a major sponsor of Hamas, and Israel and the United States worry that Gaza has become an Iranian outpost. But Mr. Meshal said: “Iran’s support to us is not conditioned. No one controls or affects our policies.”

Asked whether his movement, a branch of the Muslim Brotherhood and Islamist in outlook, wanted to bring strict Muslim law to Gaza and the West Bank, he said no. “The priority is ending the occupation and achieving the national project,” Mr. Meshal said. “As for the nature of the state, it’s to be determined by the people. It will never be imposed upon them.”