After two days of withering and sometimes combative nuclear talks, Iran and six world powers put a positive spin on the outcome.

Both Iran and the so-called P5+1 group of world powers spoke of "some common ground" – most importantly a willingness by Iran to address its sensitive 20 percent uranium enrichment program, which is technically not far from weapons grade – that will drive the next round of talks set for mid-June in Moscow.

Yet even the official statements pointed toward a chasm of mismatched expectations that has only widened in Baghdad, in Iran's view at least.

The setback risks future deadlock that could trigger another Mideast war: Israel has threatened military strikes against Iran's nuclear program, if it is not verifiably limited to peaceful purposes.

"I think it was a complete failure, in terms of content," says an Iranian diplomat inside the talks, who spoke on condition of anonymity.

"The more they talk, the worse it gets," said the diplomat about one of the final sessions. "The atmosphere is like Baghdad's weather," a reference to the sandstorm that swept across the Iraqi capital yesterday, closing the airport.

Western demands too far beyond Iran's red lines

Behind the scenes, diplomats from all sides say the P5+1's initial demands were so far beyond Iran's oft-stated red lines – requiring a halt to all uranium enrichment including the lowest levels, for example, and shutting down Iran's deeply buried, UN-inspected enrichment site at Fordow – that Iran barely mentioned its top priority of relief from crippling sanctions, aware that it would get no traction.

The disconnect was so severe that negotiators spent much of the unplanned second day of talks trying to craft a statement acceptable to Iran.

Indeed, Catherine Ashton, the European foreign policy chief leading talks for the P5+1 (the United States, Russia, China, Britain, France and Germany), in the statement described "very intense" discussions, and noted that "significant differences remain."

Likewise, Saeed Jalili, Iran's chief negotiator and secretary of its Supreme National Security Council, told a press conference that "talks were intensive and long," and "left unfinished."

Iranian flexibility on its 20 percent enriched uranium would depend on the P5+1 recognizing what Iran considers its "undeniable right" to enrich uranium, Mr. Jalili said.

That was not part of the P5+1 offer put forward in the first session in Baghdad. A senior US official said after the talks that recognizing such a right is "obviously not something we are prepared to do."

Iran would not bow to pressure, from sanctions or negotiators, Jalili told the Monitor in an interview after the talks.

He said the goodwill created since the first round in April, which broke a 15-month diplomatic dry spell, has been jeopardized by "approaches that were really destructive" – a reference to a unanimous Senate vote on Monday to tighten sanctions, and a late-April executive order signed by President Obama to target cyber oppressors in Iran (and Syria)."To form this pathway to cooperation, they should avoid wrong attitude[s] and a destructive strategy" of more sanctions, Jalili told the Monitor. The two-track strategy led by the US and Europe grates on Iran as "illogically" seeking to both engage Iran while increasing pressure to compel Iranian compliance.

"The pressure strategy is over; it is outdated," said Jalili. "We think there are bases for cooperation, and we can find those bases of cooperation."

The senior American official, however, said the sanctions – including tougher measures like a European oil embargo coming into effect by July 1 – are key because they "increase leverage" of the P5+1 – and signaled they could be ratcheted up further. "Maximum pressure is not yet being felt in Iran," the official added.

Iranians: Package unbalanced, influenced by Israel

Those steps designed to put pressure on Tehran were portrayed in Iran as proof that the US was not serious about talking.

Iranian officials and media presented the P5+1 proposal as unbalanced, and pointed out that the most egregious demands, in their view – that Iran halt all uranium enrichment, and shut down Fordow – were mirrored those voiced by Israeli Prime Minister Benjamin Netanyahu of Israel.

Israel is the only nation in the Middle East with a nuclear arsenal, but it is not subject to UN inspection, nor is it a signatory like Iran of the Nuclear Non-Proliferation Treaty. Its leadership calls Iran's program an "existential threat" that must be eliminated.

"I would have expected nothing but the Iranians to say that the [P5+1] package was unbalanced," the senior US official said earlier. "This is a negotiation: We each want to get the most and give the least. That's how negotiations begin."

UN resolutions require Iran to suspend enrichment

Iran is required by a number of UN Security Council resolutions to suspend all enrichment, until it clears up questions about possible weapons-related work.

But with 9,000 centrifuges installed in Iran and a growing stockpile of low-enriched uranium, many experts believe that demanding full stoppage is a deal breaker. Iran's supreme religious leader Ayatollah Ali Khamenei – who will make any final decision on P5+1 deal – says nuclear weapons are a "sin" and unIslamic, and officials insist they only want a civilian nuclear program for energy and medical research.

At the Baghdad talks this week, Iran presented its own counterproposals, which included non-nuclear issues such as civil unrest in Syria and Bahrain, and even counter-narcotics.

But it was the "illogic" of the dual-track position that the Iranian team considers a "miscalculation" that will hinder progress, says the Iranian diplomat.

"Jalili told the [P5+1]: 'You are repeating the same mistakes,'" said the Iranian diplomat. "He believes these [added pressures] are destructive to the talks, and should be stopped."

Iranian negotiator to Shiite shrines; US negotiator to Israel

The final statement in Baghdad reaffirmed the magic words from the Istanbul meeting that talks would be based on a "step by step approach and reciprocity."

Yet while the Iranians say they expected simultaneous steps of equal value, the other side made clear it expected Iran to take critical steps for some incentives, but with easing of sanctions only a distant prospect.

The original draft made no mention of Iran's right to enrich.

"They provided a draft, wishing that they include only the 20 percent," says the Iranian diplomat. It "was furiously responded to by Jalili, [who said] if they read this statement [publicly], we're going to state that the whole story was a failure, a fiasco, and he was completely angry."'

After a P5+1 huddle, another plenary session was agreed. When the talks finally ended after dark yesterday, Ms. Ashton spoke to the press for less than eight minutes, before most of the P5+1 delegations raced for the airport.

Within hours, Jalili and the Iranian team were driving south toward the Shiite holy shrine cities of Karbala and Najaf. Jalili had also visited a Baghdad shrine twice this week to pray.

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And today, the top American negotiator, US Undersecretary of State for Political Affairs Wendy Sherman, traveled to Israel, to reassure the Jewish state that its security was a top US concern.

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