Western diplomats claimed modest progress Saturday after more than 10 hours of talks with Iranian officials, raising hopes for at least a temporary easing of a nuclear crisis that has fueled fears of a new military conflict in the Middle East.

The day-long talks at an Istanbul conference center did not yield an agreement on specific curbs to Iran’s nuclear program, but U.S. and European officials described the negotiations as “constructive and useful” and said a second round had been set for May 23 in the Iraqi capital, Baghdad.

“We want now to move to a sustained process of serious dialogue,” said Catherine Ashton, the European Union’s foreign policy chief and lead negotiator for a bloc of six world powers engaged in the first direct nuclear talks with Iran since January 2011.

A senior U.S. official described the tone of the discussions as encouraging but stressed the need for rapid progress on steps to ease concerns about Iran’s nuclear intentions.

“While the atmosphere today was positive, and good enough to merit a second round, there is urgency for concrete progress, and the window for diplomatic action is closing,” said the official, who spoke on the condition of anonymity to describe diplomatic deliberations. The official added that there were no expectations for immediately lifting sanctions against Iran.

The chief Iranian representative, Supreme National Security Council Secretary Saeed Jalili, called the talks a “success” and said he believed the atmosphere was now conducive to progress.

“We saw a positive approach,” said Jalili, speaking through an interpreter. “We consider it a step forward. For Iranian people, the language of threats and pressure don’t work. But the approach of cooperation and talk could be fruitful.”

The senior U.S. official said that during the meetings, Jalili “repeated what they said in the past, that it is un-Islamic to have a nuclear weapon.”

Both Ashton and Jalili said the two sides would begin work immediately on an arguably harder task: drafting concrete proposals for resolving the crisis. The proposals and counterproposals will address an array of complex and emotionally laden issues, including Western demands for suspension of parts of Iran’s nuclear program as well as Iranian calls for easing economic sanctions.

Signaling Iran’s intention to take a tough line in the future talks, Jalili said Tehran would insist on having “full rights under the non-proliferation treaty,” implying that it will continue to maintain its right to enrich uranium, which it says it needs for peaceful nuclear energy uses. Before taking the podium, Jalili’s aide displayed a poster of Iranian scientists killed in bomb attacks over the past four years — assaults Jalili denounced as terrorism.

In addition to the Iranians and E.U. officials, the talks included high-ranking delegations from the six countries known as the P5-plus-one — the five permanent members of the U.N. Security Council, which are the United States, Britain, China, France and Russia, plus Germany. The diplomats met for 2 ½ hours in the morning then decided to continue the meetings through the afternoon and evening.

Getting Iran to agree to a diplomatic process was itself “a real achievement and probably the result of a lot of pressure and a determined effort,” said Michael Adler, a public policy scholar at the Woodrow Wilson International Center for Scholars in Washington who is focused on the Iranian nuclear crisis.

“But it’s just a prologue, not even a first chapter,” he said. “Let’s see if a real start can be made in Baghdad in reining in both Iran’s nuclear ambitions and the quasi state of war against them.”

U.S. and European officials had sought to lower expectations for the talks, the first since the disastrous meeting in January last year in which Iranian officials refused to discuss their country’s nuclear program. In the 15 months since, Iran has been hit with multiple rounds of sanctions and a European oil embargo set to take effect on July 1.

While diplomats welcomed the chance for continued dialogue with Iran, the prospect of extended negotiations carries political risks for the White House. Israeli and Arab leaders have warned that Iran may use them as a stalling tactic or a means to divide public opinion. Fruitless negotiations could also leave President Obama vulnerable to attacks from Republican opponents who have sought to portray the administration as soft on Iran.

The administration has insisted that there is still time for a diplomatic settlement, warning that a unilateral military strike on Iran’s nuclear facilities could trigger a regional war. But current and former U.S. officials acknowledged that pressure from hard-liners on both sides could undercut efforts to reach a compromise.

“The stakes are too high and the risks too great to allow for domestic politics to undermine what will clearly be a challenging set of discussions,” said Joel Rubin, a former State Department official and policy director for the Ploughshares Fund.

Saturday’s talks left unresolved key questions about precise steps Iran may be willing to take to ease Western concerns about its nuclear program. In the past, U.S. officials have floated proposals that would require Iran to halt uranium enrichment at the newly built Fordow plant, which is built beneath a mountain near the ancient city of Qom. Other proposals call for suspending all uranium enrichment until Iran agrees to aggressive inspections and other curbs to guarantee that none of its enriched uranium is used in the future to make nuclear bombs.

Western governments are also urging Iran to admit it had a secret nuclear weapons program in the past and to stop producing a more purified form of enriched uranium that can be quickly converted to weapons-grade fuel. Iran insists that its nuclear program is entirely peaceful.

The playing down of expectations before the start of the talks was an acknowledgment of the distrust that has defined relations between Iran and Western powers for decades, current and former U.S. officials said.

“Nobody knows exactly how to make a deal on the nuclear issue,” said Aaron David Miller, a former State Department official and a veteran of Middle East negotiations. “But none of the three prospective combatants [Israel, Iran and the United States] wants a regional Armageddon, and that’s why a negotiating process is king and will rule for much of 2012.”