* Pressure to free Green Movement leaders after nuclear deal
* Hardliners wary of boosting moderates before elections next year
* Khamenei may lift house arrest to heal rifts from 2009 unrest
By Babak Dehghanpisheh
BEIRUT, Aug 27 (Reuters) - Having struck a historic nuclear deal to end decades of enmity between Iran and the West, President Hassan Rouhani faces a fresh challenge at home, to win the release of leading political prisoners whose case has polarized the Islamic Republic.
Former presidential candidates Mir Hussein Moussavi and Mehdi Karroubi, along with Moussavi's wife Zahra Rahnavard, have been under house arrest since 2011.
Securing the release of the high profile trio would fulfill one of Rouhani's biggest campaign promises two years ago, but it is fraught with risks and could lead to an outright showdown with Iranian hardliners, experts say.
Just how important the issue is to Rouhani's supporters was made clear after the announcement of the nuclear deal last month, when people celebrating in the streets of Tehran held up pictures of Moussavi and Karroubi and chanted for their release.
The two men, who both ran against Mahmoud Ahmadinejad for Iran's presidency in the disputed 2009 elections, came to be seen as figureheads of the country's reformist "green movement".
Hardliners refer to them as "sarane fetne", or the "leaders of sedition" and have refused any compromise on their release because they are seen as a threat to national security.
Some hardline clerics and politicians have even suggested they should be executed.
"The political risks are great. The hardliners still control parliament. They control the security and intelligence forces. They control the apparatus which has been instrumental in keeping these individuals under house arrest," said Faraz Sanei, the Iran researcher at Human Rights Watch.
By contrast Rouhani's authority, centred on the cabinet and his presidential office, has only limited influence over whether to extend or end the reformists detention, he said.
Moussavi, Karroubi and Rahnavard - a prominent academic who campaigned alongside her husband - were blamed for stoking the unrest after the disputed 2009 presidential election in which Ahmadinejad was declared the winner.
But it was two years later, after Moussavi and Karroubi called for street protests in solidarity with the 2011 Arab uprisings, that the trio were placed under house arrest.
Their detention is an ongoing reminder of the deep rift created in Iranian society, sometimes dividing households, by the street violence and arrests following the 2009 elections. The issue has even led to heated debates between hardline and moderate politicians within the Iranian parliament.
FAMILY PLAYS DOWN CHANCES OF RELEASE
Until now, no security agency or individual has taken responsibility for the house arrest, though members of the opposition say it is a result of a direct decision by Supreme Leader Ayatollah Ali Khamenei, the country's highest authority.
All three have had serious health problems while under house arrest and have been hospitalized more than once.
Despite the boost that Rouhani received from the nuclear deal, it is unlikely that Moussavi, Karroubi and Rahnavard will be released in the short term, Karroubi's son Mohammad Taghi said in an interview from Britain.
He pointed to two key elections coming up next year: majles, or parliament, and the Assembly of Experts, a body that selects the Supreme Leader.
Given the 76-year old Khamenei's health woes - he had prostate surgery last year - it is likely that this Assembly, which will sit for eight years, will choose his successor.
"Lifting the house arrest might increase the capabilities of the reformists and other groups and strengthen their hand in the elections," said Taghi. "They don't want to create a situation where the hardliners will have a greater loss."
The political threat from reformists, many of whom were arrested or harassed by security forces after the 2009 election unrest, increased last week when the first meeting of a new political party was held.
Dozens of prominent reformists, out of the limelight since the 2009 election, attended the inaugural meeting of the Union of Islamic Iran People Party, which is expected to put forward candidates at next year's parliamentary election.
None of the attendees mentioned the detained trio in speeches but some of those at the meeting last Thursday lobbied Rouhani about the issue during a meeting in June, according to the opposition Kaleme site.
Other prominent politicians and clerics have also spoken up about the case. Some supporters of the trio have been targeted in recent months.
In March, parliamentarian Ali Mottahari, who has brought up the issue in parliament repeatedly, was attacked in Shiraz by a motorcycle mob who broke the windows of his car.
When one of Karroubi's former spokesmen, Esmail Gerami Moghaddam, returned to Iran after six years of self-imposed exile in July he was arrested at Tehran airport and transferred to Evin prison, according to a report by the International Campaign for Human Rights in Iran.
PRESSURE WILL INCREASE
As the nuclear deal increases Iran's interaction with the world, there will likely be more pressure for the release of Moussavi, Karroubi and Rahnavard, experts say.
But the key will be Khamenei. In the past, when the Iran's vital security or economic interests have been threatened - as with sanctions over the country's nuclear programme - Khamenei has shown himself to be pragmatic, experts say.
Rouhani could appeal to that pragmatism by arguing that releasing the trio could help tamp down internal tensions and stabilize the Islamic Republic.
"Rouhani comes from the core of the establishment. He thinks that if you open up the system it will make the system more durable," said Ervand Abrahamian, a professor of Iranian and Middle Eastern history at the City University of New York.
"And to do that it make more sense to open up and bring in the reformers into the regime rather than having them in opposition."
If the issue of the house arrest of Iran's most prominent political prisoners is not addressed, the serious divisions created by the unrest in 2009 will continue, experts say.
"In terms of the political consciousness, those individuals are on the minds of everyday Iranians," said Sanei from Human Rights Watch. "As long as that issue is not resolved and those people continue to be in limbo I think that open wound continues to fester for hardliners, reformists or ordinary Iranians who are not necessarily political in any way."
(Reporting By Babak Dehghanpisheh; Editing by Dominic Evans) ((email@example.com;)) <