* U.S. seeks "critical choices" from Iran in nuclear dispute
* Extension of negotiations is possible for up to 6 months
* But Western diplomats say progress needed for extension
* Zarif: Iran's team will work hard for deal in coming days (Adds Kerry quotes, White House statement, EU comment)
By John Irish and Fredrik Dahl
VIENNA, July 14 (Reuters) - U.S. Secretary of State John Kerry said he held good and serious talks with his Iranian counterpart on Monday as the two sides raced to narrow wide gaps on Tehran's nuclear programme less than a week before a July 20 deadline to reach a deal.
Seeking to push Iran to make "critical choices" over its disputed atomic activities, Kerry met Mohammad Javad Zarif for a second day running with both sides complaining ahead of the gatherings that scant progress had been made.
"We are working. We are working very hard. A lot of serious discussions. It was a good meeting," Kerry told reporters after ending a session with Zarif and European Union foreign policy chief Catherine Ashton.
They are trying to bridge major differences in negotiating positions over a deal intended to end a decade-long dispute over a nuclear programme which Tehran says is peaceful. The West fears it may be aimed at developing nuclear weapons capability.
In Washington, the White House said Iran had engaged with Western powers in a serious way, but had yet to make the decisions necessary to prove that the programme was peaceful.
Spokesman Josh Earnest, asked whether Kerry was authorised to extend the deadline, said he was assessing Iran's positions and would return to the United States to make recommendations to President Barack Obama on how to proceed.
A senior U.S. State Department official said Kerry, Ashton - who is coordinating discussions with Iran on behalf of six world powers, including the United States - and Zarif had a "lengthy and productive meeting", but that more work was required. It was unclear whether Kerry and Zarif would meet again on Tuesday.
The powers, also grouping Britain, China, France, Germany and Russia, want Tehran to significantly scale back its nuclear enrichment programme to make sure it cannot yield nuclear bombs.
Iran's priority is to get sanctions that have severely damaged its oil-dependent economy lifted as soon as possible.
With the differences over pivotal issues including Iran's enrichment capacity still large, some diplomats and experts have said a deal by July 20 is unlikely and that the sides will need to extend the negotiating period.
However, Ashton's spokesman Michael Mann told reporters that they were still trying to strike a deal by the target date.
"We are determined to try and get an agreement by July 20. There are still significant gaps and we are trying to narrow those down ... we still have some time. There is a text and there are still brackets around the main issues."
Before Monday's meetings, a senior State Department official said Kerry wanted to "gauge Iran's willingness to make the critical choices it needs to make".
Kerry said on Sunday there were still substantial differences with Iran on how to curb its nuclear fuel-making capacity, a view Iranian and other Western officials echoed.
Earlier, a senior U.S. official said Iran was sticking to "unworkable and inadequate" positions.
A history of hiding sensitive nuclear work from U.N. inspectors has kept international suspicions about Iran's nuclear programme high and heightened the risk of a new Middle East war should diplomacy fail to yield a long-term settlement.
EXTENSION OF TALKS?
Zarif said on Sunday after his meeting with Kerry that "our team is ready to work with full speed during the seven remaining days in order to reach a comprehensive deal that can be acceptable for both sides".
But with the two sides so far apart there was little optimism that an agreement could be signed by next Sunday. The thorniest issue, diplomats close to the talks say, is the size of Iran's future enrichment programme.
"It will be difficult to have an agreement in a week," a senior Western diplomat said. "The Iranians would have to budge on the key issues and very quickly. There are a lot of technical aspects that would be difficult to complete in a week."
There is a possibility that the talks on a long-term settlement could be extended for as long as six months.
A Nov. 24 preliminary agreement between Iran and the six powers included a provision for lengthening talks on a permanent agreement as far out as next January if all sides agree. But even an extension would have to be negotiated.
"The question will be, do we continue to talk and for how long?" the Western diplomat said.
A senior U.S. official said on Saturday that an extension would be difficult to consider without first seeing "significant progress on key issues".
Western officials have said that major hurdles include enrichment, Iran's stockpiles of nuclear material and answering U.N. inspectors' questions about its past atomic research that Western powers and analysts suspect was linked to weapon-making.
French Foreign Minister Laurent Fabius on Sunday publicly raised the possibility of extending the talks, though British Foreign Secretary William Hague said it was too early to discuss the idea of an extension. (Additional reporting by Parisa Hafezi, Lesley Wroughton, and Louis Charbonneau; Writing by Louis Charbonneau; Editing by Mark Heinrich)
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