(Adds quote from pro-Abdallahi politician, Nouakchott calm)

By Hachem Sidi Salem and Vincent Fertey

NOUAKCHOTT, Dec 21 (Reuters) - Mauritania's military junta on Sunday freed from house arrest ousted President Sidi Mohamed Ould Cheikh Abdallahi, who vowed to fight to return to the office he lost in a bloodless coup in August.

The generals who overthrew Abdallahi, the first democratically elected president of the west Saharan Islamic state, had said this month they would release him as part of negotiations to head off threatened European Union sanctions.

Former colonial power France, which holds the rotating EU presidency, welcomed the release but reiterated the international community's demand that the ousted president be restored to office. "The solution to the current crisis is a return to constitutional order," it said in a statement.

Mauritania's coup leaders have refused to reinstall Abdallahi, who won multi-party elections last year.

The ousted president was freed after he was driven to the dusty coastal capital by security officers from his hometown of Lemden, 200 km (125 miles) to the south. He later returned to Lemden with friends, supporters said.

In an interview published on Sunday by the French newspaper Le Monde, Abdallahi said he considered himself "the legitimate, democratically-elected president".

"I'll push my freedom to the limits the coup leaders put on it. I am firmly resolved to fight to make this coup d'etat fail," he said in the interview, which was conducted shortly before he was freed from house arrest.

Abdallahi told Le Monde he would make political contacts at home and abroad and could try to attend the next summit of African Union leaders at the end of January in Addis Ababa.

His daughter Amal Mint Cheikh Abdallahi said his release "was not a real freedom". "I doubt he'll be allowed to leave the country," she told Reuters.

Abdallahi supporters described the release as an attempt by junta chief General Mohamed Ould Abdel Aziz, who led the Aug. 6 coup, to avoid more sanctions against Mauritania, the world's No. 7 iron ore exporter and an oil producer since 2006.

"The fight today ... is not whether Abdallahi is detained or released ... but his return to the presidential chair," said Jemil Ould Mansour, an Islamist politician and member of the pro-Abdallahi National Front for the Defence of Democracy.

Nouakchott's streets were calm on Sunday and there were no demonstrations for or against the ousted president.

TARGETED SANCTIONS

The European Union and the United States, which view Mauritania as a valuable ally in the war against Islamist militant groups in the Sahara, have strongly condemned Abdallahi's overthrow and are pushing for his reinstatement.

On Nov. 21, the EU threatened individually targeted sanctions against Abdel Aziz and members of his military administration if they did not restore constitutional rule.

The EU says it will avoid sanctions that hurt Mauritania's 3 million people and continues to pay Nouakchott more than $100 million a year for fishing rights, underpinning the budget.

On Friday, the United States said it would axe trade benefits for Mauritania as of Jan. 1 in response to the coup. Washington has cut back military and non-humanitarian aid since the coup and banned junta members from entering the U.S.

Junta chief Abdel Aziz has promised to hold presidential elections and has announced a process of national consultations starting Dec. 27 to discuss the transition to the polls.

But Abdallahi, though invited, refused to take part. "I'm saying categorically 'No'! If I said yes, that'd be legitimising the coup and accepting the fait accompli," he told Le Monde.

Although there have been some pro-Abdallahi demonstrations, a wide section of Mauritania's political establishment supported the coup. Critics said his government was elitist and did little to shield the population from rising fuel and food prices. (For TIMELINE of Mauritania click on [ID:nLL418865] ) (For full Reuters Africa coverage and to have your say on the top issues, visit: http://africa.reuters.com/) (Additional reporting by James Regan in Paris; Writing by Pascal Fletcher and Dan Magnowski; editing by Michael Roddy)

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