* Large crowds turn out in Bamako and Timbuktu
* Vote needed for nation to move on from war, coup
* Islamist threat lingers despite French-led offensive
Malians turned out in large numbers to vote on Sunday in a presidential election they hope will provide a fresh start for the West African nation after more than a year of turmoil, war and an army coup.
From the lush, bustling riverside capital, Bamako, to the northern desert town of Timbuktu, voters crammed into schools turned into polling stations for the day, protected by Malian, French and United Nations forces.
A successful vote on Sunday would mark a major step towards recovery after a March 2012 coup followed by the occupation of the desert north by separatist Tuareg rebels and al Qaeda-linked fighters. Months ago the Islamists were marching south, until French troops arrived in January and defeated them, scattering them into the deserts and mountains.
High turnout out at 21,000 polling stations would breathe life into Mali's 20-year-old democracy, whose frailties were exposed by the coup last year.
"I came to choose a president capable of managing the country," said Mamoutou Samake, 46, an agricultural engineer and the first to vote at a polling centre in Bamako's Banankabougou neighbourhood.
"The priority of the new president must be to reestablish peace and security. The rest will come with time," he said.
After some initial delays in deploying voter material, voters carrying ID cards formed long lines in the dirt courtyards of schools by mid-morning. Many women, most in colourful traditional dress, brought their children to polling stations.
"I have worked in eight elections and I have never seen this level of turnout," said Mahamar Maiga, an election worker.
Turnout for a presidential election in Mali has never exceeded 40 percent.
In the northern desert town of Timbuktu, seized by al Qaeda-linked rebels last year, Malian soldiers manned checkpoints. People turned out in large numbers despite a threat from an Islamist group to attack polling stations. By early afternoon, no incident had been reported.
"We are still scared. We don't know who is who, there could be jihadists among the population," said Maty Balkissa Toure, a 25-year-old Timbuktu resident. "But we are proud of being Malian and risking our security to come and vote."
In Kidal, where just 30,000 votes are at stake but the stand-off with Tuareg MNLA rebels has not yet been resolved, residents reported high security and a much lower turn out. A handful of supporters of the MNLA rebel group led a small protest against the vote despite the group saying it supported elections.
Mali's 6.8 million registered voters will choose from 26 men and one women. The field includes two former prime ministers - Ibrahim Boubacar Keita, known universally as IBK, and Modibo Sidibe - who are expected to be among the top finishers.
Soumaila Cisse, a respected economist, former finance minister and native of the region of Timbuktu, is also among the leading candidates. And relative political newcomer Dramane Dembele, chosen as the candidate of Mali's largest party, ADEMA, could appeal to young voters.
Most of the front-runners are established political figures from the last 20 years of Malian politics so there is little likelihood of a radical overhaul despite calls for change after the unprecedented crisis in the former French colony.
A second round is due to take place on Aug. 11 if no candidate wins more than 50 percent of the vote.
World powers, led by France, have been pushing for the vote to be held to replace the weak interim administration that has led the country since April 2012. Some experts had warned that a rushed election might lead to challenges and further crises.
But election officials say they have distributed 85 percent of the ID cards on time.
"A month ago, there were a lot of doubts. But it has come together," U.S. Ambassador Mary Beth Leonard told Reuters.
"LAW OF MAJORITY"
Reuters journalists witnessed some voters struggling to find the right polling station or complaining their names were not on lists even though they were carrying the correct ID cards.
But Mali's interim President Dioncounda Traore said the vote had been the best the country had organised since independence.
"Democracy is the law of the majority. I ask that all candidates accept the result of the ballot boxes," he said.
The APEM network of 2,100 Malian election observers said in a statement that 96 percent of polling stations had opened on time and turnout was "high", without giving further details.
Before last year's collapse, Mali, a poor nation straddling the south of the Sahara, had built up a reputation for stability and become Africa's No. 3 gold producer.
Donors who slashed aid after the coup have promised more than 3 billion euros in reconstruction assistance after the election.
The new president will have to oversee peace talks with separatist Tuareg rebels who have agreed to allow the vote to take place in areas they operate in but have yet to lay down their arms.
France is hoping a successful vote will allow it to scale down its military presence in Mali from around 3,000 troops. A 12,600-strong U.N. mission is rolling out.
Donors are hoping that by voting in large numbers Malians will revive a democracy that was envied abroad as a model of stability but failed to mobilise enthusiasm at home, fostering a corrupt, weak system that lacked checks and balances.
"This rebellion and the coup may have taught us a lesson that we need to build a proper democracy," said Gossy Dramera, a member of parliament, before he looked for his polling station.