(Recasts with Abdallahi interview, daughter, EU comment)
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 recalled its 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 told by authorities in Nouakchott he was being freed after he was driven to the coastal capital by security officers from his home town of Lemden, some 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.
But while his supporters celebrated, his daughter Amal Mint Cheikh Abdallahi said his release "was not a real freedom". "I doubt he'll be allowed to leave the country, for example, if he's invited to a heads of state summit," she told Reuters.
There was no immediate comment from the ruling military High Council of State headed by General Mohamed Ould Abdel Aziz, who led the Aug. 6 coup in Mauritania, the world's seventh biggest iron ore exporter which became a modest oil producer in 2006.
TARGETED SANCTIONS
The European Union and 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 return.
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 over $100 million a year for fishing rights, underpinning the state 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 country.
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.
Abdel Aziz and three other top military commanders overthrew Abdallahi in August hours after he ordered their sacking.
"If I have one regret, it's that I waited too long to sack the four of them," Abdallahi told Le Monde. (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 Sami Aboudi)
Sidi Ould Cheikh Abdallahi.

Mauritania's President Sidi Ould Cheikh Abdallahi has been freed "without conditions" from house arrest by the military junta on Sunday.

Sidi Mohamed Ould Cheikh Abdallahi (Arabic: سيدي محمد ولد الشيخ عبد الله) is a Mauritanian politician who served in the government during the 1970s, and after a long period of absence from politics he won the March 2007 presidential election, taking office on 19 April 2007. He was deposed in a military coup d'etat on August 6, 2008. 

He was removed from Lemden to his soldiers guarded private residence in Nouakchott (Arabic: نواكشوط or انواكشوط), the Capital and by far the largest city of Mauritania. It is one of the largest cities in the Sahara. The city is the administrative and economic centre of Mauritania.

Sidi's release is a result of protracted and intense international pressure on the ruling military High Council of State headed by General Mohamed Ould Abdel Aziz, to restore constitutional rule to the nation. France and the US had canceled their aid, while the African Union has also suspended the country due to the 6 August coup d'état. But the leaders still refused to reinstate Sidi, amid the demands of the EU, the United States and other major donors.

Nouakchott.
Reuters has reported that "the EU says it will avoid sanctions that would hurt Mauritania's 3 million people, and continues to pay Nouakchott over $100 million a year for fishing rights, underpinning the state budget." Further, the United States on Friday announced it would cut trade benefits for Mauritania as of January 1. 

It is expected that Sidi will be allowed to participate in a "national consultation meeting" on December 27. But in an interview by the French newspaper Le Monde, he said that "participating in the December 27 talks would be to legitimise the coup d'état".