* No reply yet from six world powers at Geneva talks
* Iran says proposal "serious", "logical", no details yet
* As sanctions bite, Iran says it's eager for swift deal
* Israel urges powers not to relax sanctions prematurely
* Talks seen as biggest chance in years to resolve stand-off
* Atmosphere brighter since moderate Iran president elected
By Justyna Pawlak and Yeganeh Torbati
GENEVA, Oct 15 (Reuters) - Iran said it presented a "logical" proposal in talks with six world powers on Tuesday aimed at achieving a breakthrough in a decade-old standoff over its contested nuclear programme that has raised the risk of a new Middle East war.
The Islamic Republic began negotiations in earnest with the United States, Russia, China, France, Britain and Germany two months after President Hassan Rouhani took office promising conciliation over confrontation in relations with the world.
After years of ideological defiance, Iran appeared keen for a negotiated settlement to win relief from sanctions that have crippled its economy, slashed 60 percent of its daily oil export revenue and wrought a steep devaluation of its rial currency.
Details of the Iranian proposal - unveiled as a nearly hour-long PowerPoint presentation - were not immediately available.
Western diplomats have cautioned in the past Tehran has refused to offer sufficient nuclear concessions to secure a deal. But both sides signalled that the atmosphere, at least, in Tuesday's initial session was positive.
Iranian Deputy Foreign Minister Abbas Araqchi said the global powers had a "welcomed" Tehran's proposals and the substantive details would be discussed later in the day.
"We think that the proposal we have made has the capacity to make a breakthrough. We had a very serious and good meeting this morning," he told reporters. "The questions that were asked regarding Iran's plan were completely serious and our answers were as well."
The West suspects Iran is trying to develop the means to make nuclear weapons behind the screen of a declared civilian atomic energy programme. Tehran denies this but its refusal to limit activity applicable to producing atomic bombs, or to permit unfettered U.N. inspections, has drawn severe sanctions.
In a possible sign of the Islamic Republic's determination to meaningfully address specifics of the powers' concerns, the talks in Geneva were conducted in English for the first time.
A spokesman for the European Union foreign policy chief, Catherine Ashton, who oversees diplomacy with Iran on behalf of the powers, described the Iranian presentation as "very useful" in a carefully-worded comment that appeared to signal Iran has gone further than in the past in its willingness to engage.
A senior U.S. State Department official said negotiators would be "looking at further details" of the Iranian proposal in an afternoon session on Tuesday, hinting that it was being treated as incomplete by Western diplomats.
On a personal level, the talks were complicated for Iran's chief negotiator, Foreign Minister Mohammad Javad Zarif, by persistent back pain, which landed him in hospital last week. Returning to his hotel from preliminary discussions, Zarif declined to speak to reporters, saying: "I'm really in pain."
On the eve of the talks, Washington held out the prospect of quick sanctions relief if Tehran acted swiftly to allay concerns about its nuclear programme, although both countries said any deal would be complex and take time.
At the core of the dispute are Iranian efforts to enrich uranium to 20 percent fissile purity, a technological advance that brings it close to producing weapons-grade fuel.
Iran has previously spurned Western demands that it abandon such work as an initial step to build confidence in return for modest sanctions relief, and repeatedly called for the most painful limits on trade, such in the oil sector, to be lifted.
Western diplomats have said their demands related to 20-percent uranium must be addressed before further progress is made. But some diplomats acknowledged ahead of the Geneva talks that their initial offer to Iran might be changed substantially depending on what concessions Iran offers.
In comments made to Iranian media, Araqchi said that any final deal should eliminate sanctions on Iran and enshrine its "right" to refine uranium, according to the ISNA news agency.
A U.S. administration official said any potential sanctions relief would be "targeted, proportional to what Iran puts on the table. No one should expect a breakthrough overnight".
Israel, Iran's arch-enemy and widely assumed to harbour the Middle East's only nuclear arsenal, has warned the West not to dilute sanctions before Iran has tackled core concerns - enrichment and lack of transparency - about its nuclear goals.
Israel's security cabinet pressed the powers on Tuesday to demand a complete rollback of Iran's enrichment programme - something some Western diplomats say may no longer be realistic given its size and identification by the Iranian leadership with national pride and sovereignty.
Since 2006, Iran has rebuffed U.N. Security Council demands that it shelve enrichment and has continued to expand its nuclear fuel programme, triggering ever stiffer sanctions.
Hopes of a negotiated settlement of the dispute rose last month when President Barack Obama and Rouhani spoke by telephone, the loftiest U.S.-Iranian contact since Iran's Islamic Revolution in 1979.
Washington and Tehran have been locked in mutual hostility since diplomatic relations were broken in 1980 - an estrangement regarded as a significant barrier to any nuclear deal and indeed any wider breakthrough to stabilise the volatile Middle East.