(Adds background, quotes; paragraphs 4, 6-8) Iran has freed an...

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Iran has freed an Australian couple detained for more than three months and dropped all charges against them, Australia's Foreign Minister Marise Payne said on Saturday.

The couple, identified by the ministry as Australian Mark Firkin and British-Australian Jolie King, were said by media to have been detained over accusations of flying a drone without a permit.

"The ordeal they have been through is now over, they are being reunited with their loved ones," Payne told a televised news conference.

The arrest came amid a standoff between Western powers and Iran after the United States withdrew from a nuclear deal with Iran and imposed sanctions on it, aiming to halt its oil exports.

A third British-Australian, identified earlier by her family as University of Melbourne academic Kylie Moore-Gilbert, has not been released. She has been in detention for a year.

In September, Iran's semi-official Fars news agency quoted a judiciary spokesman as saying the three Australians had been detained for spying.

Moore-Gilbert's case was complex, Payne said. "We are continuing our discussions with the Iranian government," she added. "We don't accept the charges upon which she was convicted and we will seek to have her returned to Australia."