President Barack Obama struck an upbeat tone Tuesday in a speech to the United Nations General Assembly. But he also fairly warned that the United States “will not tolerate the development or use of weapons of mass destruction.”

That notice clearly applies to not just Syria but Iran, which has long been working toward a nuclear arsenal.

And while Iran’s new president, Hasan Rouhani, delivered a generally harmonious message of his own in a speech at the U.N. later Tuesday, that doesn’t mean his Islamic republic — the world’s No. 1 state sponsor of terrorism — should be trusted.

No, Mr. Rouhani, a Muslim cleric who became president last month, hasn’t indulged in the vicious anti-American rhetoric routinely produced by his predecessor, Mahmoud Ahmadinejad.

And Mr. Rouhani did make an appeal at the U.N. Tuesday for “dialogue over conflict and moderation over extremism.”

But how can the world trust Iran to stop advancing toward nuclear weaponry when it still refuses to admit that such a program even exists?

President Obama correctly stressed Tuesday that Iran’s “conciliatory words will have to be matched by actions that are transparent and verifiable.”

Similar concerns shadow the tentative international deal, brokered by Russia, for the Syrian government to turn over all of its chemical weapons.

Mr. Obama said Tuesday: “Agreement on chemical weapons should energize a larger diplomatic effort to reach a political settlement within Syria.”

Until recently, though, Syrian President Bashar al-Assad denied having chemical weapons. Then two weeks ago, facing the imminent threat of U.S. air attacks, Mr. Assad finally acknowledged having those weapons — though he still denies using them on Syrian civilians.

And President Obama has repeatedly cited the Syrian regime’s Aug. 21 slaughter of roughly 1,400 civilians as grounds for using U.S. military force against it.

So if we can’t trust Mr. Assad to tell the truth about that massacre, how can we trust him to turn over all of his chemical weapons?

During his 50-minute address Tuesday, President Obama also voiced renewed hope for restarting peace talks before Israel and the Palestinian Authority. He said, “America’s diplomatic efforts will focus on two particular issues: Iran’s pursuit of nuclear weapons and the Arab-Israeli conflict,” explaining that “resolving them can help serve as a foundation for a broader peace.”

Of course, Mr. Obama isn’t the first U.S. president to correctly identify the Israeli-Palestinian impasse as a critical problem in the Mideast. Nor is he the first to vow that Iran will not obtain nuclear weapons.

But lofty rhetoric won’t solve those problems. Neither will President Obama’s self-congratulatory — and debatable — declaration Tuesday that “the world is more stable than it was five years ago.”

Tell that to the Syrians and Egyptians.

Still, President Obama did the right thing by going to the U.N. to emphasize America’s continuing determination to deter Iran’s nuclear ambitions, promote Mideast peace and protect Israel.

He also did the right thing by defending the notion of American “exceptionalism” — a concept criticized by Russian President Vladimir Putin in a guest column he wrote for the Sept. 12 New York Times.

As President Obama put it Tuesday: “Some may disagree, but I believe that America is exceptional, in part because we have shown a willingness through the sacrifice of blood and treasure to stand up not only for our own narrow self-interest, but for the interest of all.”

And now, “for the interest of all,” our exceptional nation must keep making diplomatic efforts to end tragic conflicts and counter rising threats in the Mideast.

But to achieve true and lasting peace, such agreements must be based on verifiable evidence — not misplaced trust.