(Edits, adds quotes from diplomat, U.S. and EU remarks)
* Kerry, other ministers could join, but no travel plans yet
* Iran wants mention of "right to enrich" in any deal
* Diplomat: Talks were "constructive but not conclusive"
* Sceptical U.S. Senate to pursue more Iran sanctions
By John Irish, Parisa Hafezi and Justyna Pawlak
GENEVA, Nov 21 (Reuters) - Iran and six major powers have made some progress toward an interim deal to curb Tehran's nuclear programme in exchange for sanctions relief, but both sides said on Thursday they still have significant differences to overcome.
Negotiators appeared to downplay anticipation of an imminent breakthrough in the three-day talks that began on Wednesday after the United States, Russia, China, France, Britain and Germany came close to winning concessions from Iran in the last round of negotiations two weeks ago.
Several Western diplomats said there was a good chance that U.S. Secretary of State John Kerry would join foreign ministers from the other five members of the six nation group in Geneva in another attempt to nail down a long elusive deal with Iran.
One diplomat saw a "very high probability" of ministers coming to another meeting, but there were no signs that the ministers were making definite travel plans.
A senior European diplomat told reporters the ministers would only travel to Geneva if there was a deal to sign.
"We have made progress, including core issues," the European diplomat said. "Tomorrow will be important. There are four or five things still on the table" that need to be resolved.
"There are things (Iran has proposed) that are acceptable, and others that aren't," he said.
Still, he added that the atmosphere was positive, describing Thursday's meetings as "constructive but not conclusive." He said no one was suggesting the talks should be broken off and indicated they could run into Saturday.
Iran's Deputy Foreign Minister Abbas Araqchi echoed the diplomat's remarks: "We still have some different views on some points and until we get closer to final stages, the foreign ministers will not come."
Finding common ground on the contours of an accord designed to start removing the risk of Iran developing a nuclear weapons capability - an intention it denies having - has been complicated.
Under discussion is an Iranian suspension of some sensitive nuclear activities, above all medium-level uranium enrichment, in exchange for modest sanctions relief. That would involve releasing some Iranian funds frozen in foreign bank accounts and allowing trade in precious metals. The United States may also agree to relax pressure on other countries not to buy Iranian oil.
The Iranians have made clear they are most interested in resuming oil sales and getting relief from restrictions on Iranian banking and financial transactions that have crippled the oil-dependent economy.
The main disputes appear to include Iran's quest for some recognition of its "right to enrich," the major powers' demand for a shutdown of the Arak heavy-water reactor project and the extent of sanctions rollbacks on the table.
A spokesman for European Union foreign policy chief Catherine Ashton, who is coordinating the talks on behalf of the six powers, spoke on Twitter of "intense, substantial and detailed negotiations on #Iran #nuclear programme, conducted in good atmosphere."
A senior U.S. State Department official said the EU-Iranian talks "were totally focused on digging into the details of the negotiations and working to make progress."
The U.S. official said Ashton sought in meetings with Iranian Foreign Minister Mohammad Javad Zarif to close gaps between the two sides.
CRUCIAL U.S.-IRAN ENCOUNTERS
The Iranians held a brief session late on Wednesday with the U.S. delegation, headed by Under Secretary of State for Political Affairs Wendy Sherman, a senior State Department official said, without elaborating.
Despite the presence of the six powers and Ashton, it is ultimately Iran and the United States that have the power to make or break a deal, diplomats said. Relations between the two were ruptured by Iran's 1979 Islamic Revolution.
In a sign of the tensions that exist between the United States and Iran, the State Department issued one of its periodic advisories on Thursday warning U.S. citizens to weigh the risks of travel to Iran. It noted that "some elements in Iran remain hostile to the United States" and that "U.S. citizens may be subject to harassment or arrest."
Policymakers from the six major powers have said an interim accord on confidence-building steps could be within reach to defuse a decade-old stand-off and dispel the spectre of a wider Middle East war over the Islamic Republic's nuclear ambitions.
Before negotiations began in earnest on details of the proposal on Thursday, France and Iran cranked up the rhetoric.
French Foreign Minister Laurent Fabius, who spoke out against a draft deal floated at the Nov. 7-9 negotiating round, was asked by France 2 television if there could be a deal.
"I hope so. But this agreement can only be possible based on firmness. For now the Iranians have not been able to accept the position of the six. I hope they will accept it."
In what appeared to be a response targeted at France, Araqchi said: "We have lost our trust... We cannot enter serious talks until the trust is restored. But that doesn't mean that we will stop negotiations."
Asked how trust could be restored, he said: "If they (the six powers) create one front, and stick with united words."
For the six powers, an interim deal would mean Iran would have to stop refining uranium to a concentration of 20 percent - a relatively short step away from weapons-grade material - accept more exhaustive U.N. nuclear inspections and mothball the Arak reactor, a potential source of weapons-grade plutonium.
"RIGHT TO ENRICH"
Israel has lobbied hard against this formula, saying it offers Iran too much for too little by leaving its enrichment infrastructure intact.
The Israeli criticism has resonated in the U.S. Congress, where sceptics are calling for further U.S. sanctions against Tehran, something President Barack Obama's administration has warned could derail the negotiations in Geneva.
Despite the concerted diplomacy in Geneva, U.S. Senate Majority Leader Harry Reid said on Thursday he was committed to pursuing a tougher Iran sanctions bill when the Senate returns from a holiday recess early next month.
Iran has demanded that the big powers acknowledge its right to enrich uranium, something the United States, France and other Western leaders refuse to do.
Araqchi said "enrichment is our red line but we can discuss the level and the amount" of uranium to be enriched.
A senior member of the Iranian delegation, speaking on condition of anonymity, said Tehran understood that all oil and banking sanctions could not be removed "in one go" but that enrichment was a red line and "we should have a paragraph on it ... "If that element is not there, there will be no deal."
Zarif hinted at a possible way around this issue last weekend - Iran could insist on its own right to enrich uranium without requiring others to explicitly recognise it.
The interim arrangement under consideration calls for a six-month period of sanctions relief for Tehran that would give Iran and the major powers time to craft a broad, permanent accord.
The United States has said most of the sanctions will remain in place and any temporary sanctions relief would be cancelled if no long-lasting agreement with Tehran is reached, or if the Iranians violate the terms of the interim deal. (Additional reporting by Louis Charbonneau and Fredrik Dahl in Geneva, Dan Williams in Jerusalem and Arshad Mohammed in Washington; Writing by Louis Charbonneau and John Irish; Editing by Mark Heinrich and Christopher Wilson)