Slowly, but surely, relations between Iran and the West appear to be improving. Even though Iran’s new President Hassan Rouhani did not meet U.S. President Barack Obama at the United Nations General Assembly this week as some had hoped, each man signaled a desire for a rapprochement and expressed a willingness to make that happen. Improvement is possible — relations between the United States and Iran are not good — but it will take action, not just words, to make it real.

The election of Mr. Rouhani in the Iranian presidential ballot in June surprised many. He is a conservative — and indeed looks moderate only because of the outsized presence of radicals in Iranian politics — but he recognizes the increasingly untenable position his country is in and the need to change policies to ease its isolation and end the hardships that squeeze the Iranian people.

Some changes are easy. First, he must end the hate-filled rhetoric favored by his predecessor, Mr. Mahmoud Ahmadinejad. The talk of wiping Israel off the map, denying the Holocaust and denouncing Zionist plots at every turn contributed to a sense that Iran could not be trusted or reasoned with.

To his credit, Mr. Rouhani’s U.N. speech was purged of all that. He criticized the treatment of the Palestinian people, as is his right, but he did so in way that defended their rights, rather than denying Israelis their own.

More difficult will be finding a way to dispel suspicions that surround Iran’s nuclear ambitions. Tehran’s failure to assuage the concerns of the International Atomic Energy Agency (IAEA) has led to hard-hitting sanctions that are inflicting great damage on the Iranian economy.

In his speech, Mr. Rouhani reiterated Iran’s right to develop nuclear technology for peaceful purposes, and argued that the country’s program was too far advanced to be stopped by outside pressure. He repeated that Tehran has no interest in nuclear weapons in unequivocal language: “Nuclear weapons and other weapons of mass destruction have no place in Iran’s security and defense doctrine, and contradict our fundamental religious and ethical convictions.” Finally, he denounced the sanctions that victimize “the common people.”

At the same time, he said he was prepared to engage in “time-bound and result-oriented talks to build mutual confidence and removal of mutual uncertainties,” and hoped that Mr. Obama would ignore “warmongering pressure groups” and permit the U.S. and Iran to “arrive at a framework to manage our differences.”

Mr. Obama’s remarks suggested that a deal is possible. While he stuck to his basic line — “We will not tolerate the development or use of weapons of mass destruction” — he reminded his audience that “We are not seeking regime change, and we respect the right of the Iranian people to access peaceful nuclear energy.” The West wants Iran to “meet its responsibilities under the Nuclear Non-Proliferation Treaty and U.N. Security Council resolutions.”

While the much-speculated handshake between the two presidents did not occur, another important meeting did take place. On Thursday, U.S. Secretary of State John Kerry joined the E3-plus-3 talks (the five permanent members of the U.N. Security Council and Germany), which include Iranian Foreign Minister Mohammad Javad Zarif, to discuss resumption of negotiations over Iran’s nuclear program. This is the highest level meeting between the U.S. and Iran since 1980.

While the nuclear talks have been fitful and more disappointing than fruitful, Mr. Zarif said he is aiming to conclude a nuclear deal within a year. EU High Representative for Foreign Affairs and Security Policy Catherine Ashton said the parties would meet again in Geneva on Oct. 15-16.

The Tehran government has taken other steps to lower tensions. Just before Mr. Rouhani left for the U.N., it announced that 80 political prisoners would be pardoned, many of whom had been arrested in a crackdown that followed the 2009 presidential elections. While the move fulfills one of Mr. Rouhani’s campaign promises, it also signals a readiness of the new government to respond to — and actually tackle — Western concerns.

The president also promised to introduce “a citizens’ rights’ charter,” but the scope of that initiative is not yet clear. And earlier this month, the new president sent Jewish New Year’s greetings on his personal twitter account, an unprecedented gesture.

Of course, the differences remain profound. The level of transparency that the West is demanding from Tehran regarding its nuclear program will be considered intrusive. The suspicion and mistrust that dominate the relationship will magnify every disagreement and offer ample opportunities for disruption by those opposed to any improvement in relations.

Tehran remains committed to the Syrian government, its closest ally in the region, but Mr. Rouhani expressed support for putting Syria’s chemical weapons under international control. There is the fact that Mr. Rouhani is not the ultimate decision maker in Iran. That position is held by Supreme Leader Ayatollah Ali Khamenei and the president serves — and makes policy — at his pleasure.

Mr. Khamenei knows that isolation does not serve his country well. But he cannot disregard conservative interest groups that support his rule and who have their own ideas about how close Iran should move toward the West. Although Mr. Rouhani said in an interview with The Washington Post that he had the supreme leader’s full backing to broker a nuclear deal, he must navigate this triangle if he is to build sustainable relations with the West.

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