(Updates with Bouteflika back in Algeria, new quotes)
* Bouteflika suffered stroke early last year
* After ten years in power, succession still unclear
* Region unstable, elite seen avoiding upheaval
ALGIERS/TUNIS, Jan 16 (Reuters) - Abdelaziz Bouteflika's second visit to Paris for hospital treatment has reignited speculation the president who oversaw Algeria's emergence from almost a decade of civil war may be unable to run for reelection in April.
Bouteflika, a Western ally against militant Islamists in North Africa who suffered a stroke last year, flew to France on Monday for what state news agency APS called a planned check-up, saying his condition was "progressively" improving.
He had been scheduled back on Friday, the first day of the election campaign. But Anis Rahmani, a media owner close to Bouteflika, said on Thursday the president had already returned and one source described his condition as "fine".
"He is back home 24 hours before the deadline to kick off the campaign. It is a political signal that the president is ready to run a fourth term," Rahmani, owner and manager of Ennahar TV, told Reuters.
The ruling FLN party says Bouteflika, 76, is their only candidate for April's presidential election, in which he would run for a fourth term and almost certainly win due to the nationalist party's dominant role.
Any potential transition in the major North African energy supplier would come at a delicate time, with neighbouring Egypt and Libya deep in turmoil three years after "Arab Spring" revolts that ousted their long-term leaders.
"He simply cannot leave the country now because of all the regional threats," Rahmani said. "He cannot quit because the opposition is not ready to rule."
Gauging Algeria's opaque politics is complicated, observers say, with a cadre of veteran FLN party leaders and army generals known as "Le Pouvoir" or "The Power" in French, ruling behind the scenes since 1962 independence from France.
But time is running short: Campaigning starts on Friday, and candidates must register for the April 16-17 election before a constitutional deadline in February.
The Algerian leader, who spent months in a French hospital last year before returning home in July, has been quiet and clues seeping out of the ruling elite and business and political circles provide conflicting accounts.
His political opponents say he is too ill to work. Late last year he was visibly tired, two senior security sources said, and his health had deteriorated. But soon afterwards, he was seen in a live appearance receiving his chief of staff.
APS said on Thursday his health had shown "marked improvement".
Should he step aside, a handover from Bouteflika, who befriended Cold War-era icons like Fidel Castro and Yasser Arafat over his long career, is likely to be well-managed, analysts say. The FLN party-military elite alliance has vested interests in avoiding instability, they say.
While the president is elected, a Bouteflika successor may be chosen through an internal tussle between his inner circle and the DRS military intelligence service, which has played a kingmaker role since the days of civil war in the 1990s.
A source from the business elite close to the government, who asked not be identified, said Bouteflika plans to run and is expected to appoint two vice presidents, a position now being prepared, to help in his campaigning.
Analysts say some of that may be political positioning by Bouteflika's allies, to guarantee a strong hand in backroom negotiations with military rivals over any succession.
Already, Prime Minister Abdelmalek Sellal's name is touted as one potential vice president. A technocrat, Sellal managed most day-to-day governing in Bouteflika's absence last year and is seen by many as a possible "consensus" handover candidate.
Senate chairman Abdelkader Bensalah, former premier Mouloud Hamrouche and Ali Benflis, who is backed by some powerful factions in the FLN, are other names in the ring.
"A smooth transition is paramount," said Geoff Porter, director of North Africa Risk Consulting. "Although Algeria's political elite have their policy differences and back different candidates, they agree that the country cannot risk instability at this juncture."
After his return to Algeria following his stroke and Paris treatment, Bouteflika appeared only a few times in public during convalescence, meeting visiting dignitaries such as the French prime minister.
But in the last months of 2013, sources say, Bouteflika moved to solidify his influence by transferring key responsibilities away from the DRS intelligence, to weaken its position, and reshuffling the cabinet to shore up his allies.
Last week, two more top DRS generals -- in charge of domestic security and counter-terrorism -- and one colonel, were sacked, bringing the number of generals retired to four in less than a year, according to one security source.
Bouteflika's allies have also pushed for a constitutional amendment to create the position of vice president -- allowing Bouteflika associates to campaign for him in case he is too ill. His backers have a majority in the parliament, but it may be too late to get it drafted and passed.
Rumours are rife, but few details emerged in Algeria or France about the president's health. In announcing his visit to Val de Grace hospital in Paris for checkups it said were planned last year, APS said: "The president's health is improving certainly and progressively."
Should Bouteflika become too ill to continue, the current chairman of senate, Bensalah, who heads the second ruling party RND, would take over for as long as 45 days until elections.
"It is ridiculous to speak about Bouteflika running for fourth term. The man is unable to rule, the man is ill, but his inner circle continue to say he can run," leader of the moderate Islamist party MSP, Abderazak Mokri said.
"If he was in Paris only for a checkup, why not do it here in Algeria?"
If Bouteflika steps down or can no longer run for election, the vast North African country is unlikely to slide into upheaval seen in Egypt, Libya or Tunisia, whose leaders were overthrown in 2011 over economic malaise and repression.
After years of centralized state control over the economy, analysts say Algeria is certainly in need of economic reforms, and riots and protests over housing, jobs and opportunities occasionally break out in different regions of the country.
But the 1990s war that killed 200,000 people left many Algerians wary of turmoil, and the OPEC country's huge foreign reserves handed Bouteflika enough of a financial cushion to sooth potential protests over living conditions and jobs.
Algeria's global security role remains key. After Bouteflika helped end the war with Islamist fighters, Algeria has evolved into a strong ally in Washington's campaign against al-Qaeda style militants in the Maghreb.
Foreign oil companies, critical of Algeria's contract terms, will watch also transition for better incentives, especially after the militant attack on the Amenas gas plant a year ago that killed 40 oil workers.
Bouteflika himself has said it was time over for the old-guard from the independence era, but any successor will likely represent stability rather than generational change, and be backed by the ruling party establishment.
Among those who could succeed him and be seen as guardians of that continuity is premier Sellal, who is accepted by both Bouteflika's wing and military clans of the political elite, analysts say.
Senate head Bensalah may also be in the running, though if he takes over temporarily should Bouteflika be unable to govern, he will no longer be eligible for election.
Two other names are Hamrouche, a former premier who many see as an outsider and a reformer, and Benflis, who once ran against Bouteflika and who has strong backing from some influential factions within the ruling party.
Eurasia Group North Africa analyst Riccardo Fabiani said it may be too early to predict the outcome of the internal struggles within the rival factions of Algeria's elite, but no major policy shift should be expected for now.
"We expect the presidential faction and the military intelligence to finally agree on a consensus candidate over the next few weeks," he said. "Regardless of who the next president is, his policy agenda is likely to focus on a gradual process of economic liberalization over the next few years."
(Editing by Philippa Fletcher)