* Iran, six world powers hold June nuclear talks in Vienna
* Wide gaps remain with five weeks to go before July 20 deadline
* No discussion yet on any extension of talks - US official
* U.S. says may discuss Iraq with Iran on sidelines of talks
VIENNA, June 17 Iran and six world powers will try in talks in Vienna this week to narrow differences and keep alive hopes of ending a decade-old nuclear dispute by late July, despite doubts the self-imposed deadline can be met.
On the sidelines of the five-day meeting in the Austrian capital, the fast-moving crisis in Iraq could also require the attention of U.S. and Iranian diplomats. The two countries share concern over the ascendancy of militant Sunni rebels there.
With time running short if a risky extension of the nuclear talks is to be avoided, negotiators face huge challenges to bridge gaps in positions over the future scope of Iran's nuclear programme in just five weeks.
The talks, co-ordinated by European Union foreign policy chief Catherine Ashton, stumbled during the previous round in mid-May. Both sides accused the other of lacking realism in their demands and French Foreign Minister Laurent Fabius said the negotiations had "hit a wall".
Although such rhetoric may in part be a negotiating tactic, it also underlines how far the sides are from resolving a dispute that retains the potential to unleash war in the region. Israel sees Iran's nuclear programme as a threat and has in the past suggested it could launch military strikes on its sites.
The powers want Iran to significantly scale back its uranium enrichment programme, denying it any capability to move quickly to production of a nuclear bomb. Iran denies any ambition to produce such a weapon and demands crippling economic sanctions, eased slightly in recent months, be lifted entirely.
The sides also need to agree on other complex issues as part of a comprehensive deal, including the extent of U.N. nuclear agency monitoring of Iranian nuclear sites, how long any deal should run and the status of Iran's planned Arak research reactor, which could potentially yield plutonium for bombs.
"We don't have illusions about how hard it will be to close those gaps, though we do see ways to do so," a senior U.S. official said, signalling the pace of diplomacy would intensify in the days and weeks ahead.
Sounding a cautiously hopeful note after a bilateral U.S.-Iranian meeting in Geneva last week, the official said that "we are engaged in a way that makes it possible to see how we could reach an agreement", without giving details.
In Tehran, Iran's Foreign Minister Mohammad Javad Zarif said: "If the other parties enter in negotiations with realistic views, the possibility of a final agreement exists. But if they act irrationally, we will act in accordance to our national rights."
Ashton, Zarif and the U.S. delegation, led by Under Secretary of State Wendy Sherman and including Deputy U.S. Secretary of State Bill Burns, held trilateral talks on Monday ahead of the start of formal negotiations on Tuesday.
The U.S. official also said the United States may discuss the security crisis in Iraq with Iran during this week's nuclear talks, in what could mark a momentous step in U.S. engagement with its longtime adversary.
Both Washington and Tehran are alarmed by the rapid advance in Iraq of insurgents from the radical Islamic State of Iraq and the Levant (ISIL), which is seeking to re-create an Islamic caliphate across much of Iraq and neighbouring Syria.
"There may be discussion of that issue on the margins of our discussions, completely and separately apart from the nuclear negotiations," the U.S. official said.
IRAN "WANTS A LOT"
Diplomatic sources have told Reuters that it is increasingly likely Iran will seek an extension of the nuclear talks deadline. But Western officials insisted the focus was still on sealing the agreement by late next month, noting that any extension must be agreed by all sides.
"If there is an extension if will be for a few weeks," a diplomat from one of the six powers - the United States, France, Germany, Russia, China and Germany - told Reuters. If a deal were really within reach the sides shouldn't need six more months.
The seven states agreed on the July deadline to reach a comprehensive agreement as part of an interim deal on the decade-old nuclear stand-off in Geneva struck on Nov. 24.
That accord - under which Iran suspended some sensitive nuclear activities in exchange for limited sanctions relief - allowed for a six-month extension if necessary for a settlement.
It would allow up to half a year more for partial sanctions waivers and restraints on Iranian nuclear activity as agreed in Geneva. To avoid open conflict with a hawkish Congress, U.S. President Barack Obama would want lawmakers' approval to extend.
An extension would have its perils. Analysts say both sides might come under pressure from hardliners at home to toughen the terms during this extra time period, further complicating the chances of a successful outcome.
The previous round of talks in Vienna, the fourth since February, ran into difficulties when it became clear that the number of centrifuge enrichment machines Iran wanted to maintain was well beyond what would be acceptable to the West.
Refined uranium can be used to fuel nuclear power plants, Iran's stated goal, but also in a more highly refined form provide material for atomic bombs, which the West fears may be it ultimate aim.
Iran says it is Israel, a close U.S. ally, which threatens regional peace with an atomic arsenal it has never acknowledged but is widely believed to possess.
"Iran wants a lot and we are ready to only give a little. A strong capacity to enrich enables them to quickly move to an armed nuclear weapon. A weak capacity delays that substantially," a Western diplomat said.