It was Mr. Rouhani’s second major speech this week at the United Nations, where he has been engaged in a near-breathless series of appearances and interviews with the Western news media. He appears to want to send the message that he is a reasonable, practical leader who differs from his bombastic predecessor, Mahmoud Ahmadinejad, and who wants urgently to solve Iran’s protracted disputes with the West, most notably the nuclear issue.

Israel, which regards Iran as an existential threat, has repeatedly warned that it may take military action to strike at Iran’s uranium enrichment centers and other nuclear facilities that the Israelis say are part of an Iranian scheme to build a weapon.

The Iranians have frequently pointed out that they have publicly renounced nuclear arms and that — unlike Israel — Iran is a member of the International Atomic Energy Agency, the United Nations nuclear monitor. The Iranians also have countered that Israel is believed to already have an arsenal of nuclear weapons, which it refuses to confirm or deny.

According to the Arms Control Association, a nonproliferation group in Washington,Israel is suspected of having 100 to 200 nuclear warheads. Israel has said it will “not be the first country to introduce nuclear weapons in the Middle East.”

Mr. Rouhani said in his speech on Thursday that the total elimination of nuclear weapons should be the goal, particularly in his part of the world.

“Almost four decades of international efforts to establish a nuclear-weapon-free zone in the Middle East have regrettably failed,” Mr. Rouhani said in a translated version of his speech, furnished by Iran’s United Nations Mission.

“Urgent practical steps toward the establishment of such a zone are necessary,” he said. “Israel, the only nonparty to the nonproliferation treaty in this region, should join thereto without any further delay. Accordingly, all nuclear activities in the region should be subject to the I.A.E.A. comprehensive safeguards.”

Mr. Rouhani said nothing about Iran’s own dispute with the I.A.E.A., which wants access to some restricted military sites in the country to verify that Iran’s nuclear intentions are benign. He also made no reference to Iran’s stalled negotiations with the so-called P5-plus-one countries, the permanent members of the Security Council — Britain, China, France, Russia and the United States — plus Germany, on the larger dispute over uranium enrichment.

He said in the speech that the establishment of a nuclear-free zone in the Middle East would “constitute a contribution to the objective of nuclear disarmament” and called for a conference to establish such a zone, “without any further delay, with the participation of all countries in the region to avoid unwanted consequences.”

Mr. Rouhani commended Secretary General Ban Ki-moon for convening the conference. “No nation should possess nuclear weapons; since there are no right hands for these wrong weapons, as you, Mr. Secretary General, have rightly put it,” he said.