(Reuters) - Iran and world powers agreed to meet again next month to try to ease the long standoff over its nuclear work despite achieving scant progress at talks in Baghdad towards resolving the main sticking points of their dispute.

At its heart is Iran´s insistence on right to enrich uranium and that economic sanctions should be lifted before it shelves activities that could lead to its achieving the capability to develop nuclear weapons.

Western powers insist Tehran must first shut down higher-grade enrichment before sanctions could be eased.

But both sides have powerful reasons not to abandon diplomacy. The powers want to avert the danger of a new Middle East war raised by Israeli threats to bomb Iran, while Tehran also wants to avoid a looming Western ban on its oil exports.

After discussions in Baghdad extended late into an unscheduled second day on Thursday between envoys from Iran and the six powers, European Union foreign policy chief Catherine Ashton said it was clear both sides wanted progress and had some common ground, but significant differences remained.

"We will maintain intensive contacts with our Iranian counterparts to prepare a further meeting in Moscow," she told a news conference in Baghdad.

The next meeting, the third in the latest round of talks that began in Istanbul last month after a diplomatic vacuum of 15 months, will be held in Moscow on June 18-19.

Ashton leads the negotiations for the six-country group made up of the five permanent members of the U.N. Security Council - Britain, China, France, Russia and the United States - which together with Germany is known as the P5+1.

"Talks were intensive and long," Saeed Jalili, Iran´s chief negotiator and direct representative of Supreme Leader Ayatollah Ali Khamenei, said. "They were detailed, but left unfinished.

"The atmosphere of these talks was positive for the two sides to talk about their issues in a clear way," Jalili added. "We believe the result of these talks was that we were able to get to know each other´s views better and more."

While there was little if any concrete progress, the fact that the two sides agreed to continue talks was a sign of progress in itself, after more than a year of not meeting at all before the latest round of negotiations began in April.

"The two sides´ commitment to diplomacy in the absence of any clear agreement is a positive sign," said Ali Vaez, Iran expert at the International Crisis Group think-tank.

"All parties should be commended for returning to the negotiating table. (U.S. President Barack) Obama should be commended for having turned diplomacy into a process rather than the one-off meetings that existed in the past," wrote Trita Parsi, president of the National Iranian American Council.

"Both sides entered negotiations with their maximalist positions, and neither budged. Looking ahead, now the hard work begins."

Iran, the world´s No. 5 oil exporter, says it is enriching uranium only in order to generate electricity to serve the needs of a burgeoning population, and for a medical research reactor.

The skeptical powers want practical steps from the Islamic Republic to address their concerns over its nuclear program.

Chief among such concerns is Iran´s ability to enrich uranium to a fissile concentration of 20 percent. That is the nuclear advance most worrying to the West since it opens the way to reaching 90 percent, or bomb-grade, enrichment.

"Iran declared its readiness to address the issue of 20 percent enrichment and came with its own five-point plan, including their assertion that we recognize their right to enrichment," Ashton said.

IRAN INSISTS ON ITS RIGHTS

Iran says it will not exceed 20 percent and the material will be made into fuel for a research reactor.

Iran has hinted at flexibility on higher-grade enrichment but Iranian media said it would not give away its most potent bargaining chip without significant concessions on sanctions.

"We never expected to get that agreement (on 20 percent) here in Baghdad," said a senior U.S. administration official who declined to be identified due to the sensitivity of the subject.

But, he said "there is agreement to address all aspects of 20 percent as we put it on the table".

A significant difference between the two sides is Iran´s insistence on what Jalili called "an undeniable right of the Iranian nation" to enrich uranium.

"Obviously (that) was not something we were prepared to do," the official said, echoing the U.S. view that Iran does not automatically have this right under international law because, it argues, Iran has violated obligations under counter-proliferation safeguards by having hidden sensitive nuclear activity from U.N. inspectors in the past.

The United States and its allies have imposed tough sanctions on Iran´s energy and financial sectors to try to force it to compromise and open up its nuclear activities to scrutiny.

EU states are set to introduce a total embargo of Iranian crude oil purchases in July. Diplomats say the measure will not be cancelled unless Tehran acts to rein in enrichment first.

Iranian Oil Minister Qasem Rostani dismissed the threat of an oil embargo, saying Tehran´s adversaries would suffer more in the form of soaring crude prices.

"With the absence of Iran´s oil in global markets, something will happen to the global economy that will greatly reduce economic growth of developing and developed countries. The world is concerned about this issue today," Rostami said on Friday.

"I hope they (the West) understand what would happen if Iran´s oil is no longer in the market. If they are wise, they would learn from this period of time when oil prices jumped with only talks of sanctions..."

U.S. Secretary of State Hillary Clinton said there would be no let-up in sanctions against Iran, even as talks continue.

The senior U.S. official said the six powers were going to try to advance the talks "as fast as we can". But it was too early to talk about technical level or expert meetings because the broader political issues still needed to be clarified.

The official said sanctions coming into effect in coming weeks would increase leverage on Iran in the negotiations.

"Maximum pressure is not yet being felt by Iran," the official said, adding there were many other potential sanctions that remained to be employed.

WORRIES ABOUT WAR

The powers want Iran to send its more highly refined uranium abroad, close an underground plant devoted to 20 percent enrichment which is largely invulnerable to air strikes and submit to more intrusive U.N. nuclear inspections.

In return, they have offered fuel to keep Iran´s medical isotope reactor running, assistance in nuclear safety and an end to a ban on spare parts for Iran´s ageing civilian aircraft.

A senior hardline Iranian cleric was dismissive. "They keep saying Iran should take confidence-building steps. How many times should Iran do this? You have inspected our nuclear sites a number of times and have not found anything," Ahmad Khatami said in a sermon at Friday prayers in Tehran.

"The P5+1 should know that the Iranian nation is not the kind to submit to blackmail and ... that (our) people are here and are standing firm on their rights."

The Islamic Republic has repeatedly ruled out suspending all enrichment as called for by several U.N. Security Council resolutions, saying nuclear energy is a matter of national sovereignty and pride in technological progress.

(Additional reporting by Patrick Markey and William Maclean in Baghdad, Marcus George and Isabel Coles in Dubai, Zahra Hosseinian in Zurich, Fredrik Dahl in Vienna and Paul Eckert in Washington; Writing by Jon Hemming; Editing by Mark Heinrich) (© Thomson Reuters 2012. 05/25/12)