* Keita seen beating former finance minister Cisse in vote
* Winner's to-do list: peace, reconciliation, reconstruction (Adds quotes from Keita, Cisse)
By Daniel Flynn and Tiemoko Diallo
BAMAKO, Aug 11 (Reuters) - Malians voted in a presidential runoff on Sunday with former Prime Minister Ibrahim Boubacar Keita the frontrunner in an election which is critical to restoring stability after a military coup and Islamist rebellion last year.
The winner will oversee more than $4 billion in foreign aid promised to rebuild the West African nation, after France sent thousands of troops in January to break the grip of al Qaeda-linked rebels over its desert north.
He must also tackle deep-rooted corruption and forge a lasting peace with northern Tuaregs after decades of sporadic uprisings, problems that led to the overthrow of president Amadou Toumani Toure in the March 2012 coup and allowed Islamists to seize the northern two-thirds of Mali.
"Whatever the decision of the ballot box, Mali has already won," Keita, 68, told reporters after voting in the capital Bamako. "We've come together to rebuild a new Mali and give it a new destiny," said Keita, who is opposed by Soumaila Cisse, 63, a technocrat from northern Mali who headed the West African monetary union (UEMOA).
Voting is taking place at about 21,000 polling stations across the landlocked nation from the forested south, home to 90 percent of Mali's 16 million people, to the northern cities of Timbuktu and Gao, where Islamists imposed sharia law. An announcement of final results is expected in two or three days, and the constitutional court has until Friday to certify them.
A trickle of voters braved heavy rains in Bamako as voting began at 8 am (0800 GMT). But as the weather cleared, residents emerged from their homes to crowd into polling stations.
"The Malian people are tired. Our suffering has lasted long enough. Let God grant victory to the candidate who can bring us happiness again," 35-year-old housewife Aminata Traore said after voting in Bamako's Badalabougou neighbourhood.
Keita is the favorite after winning nearly 40 percent of the first-round vote on July 28, promising to impose order and restore the honour of the nation, which had been regarded as a bulwark of stability in a turbulent region.
Twenty-two of the 25 losing first-round candidates have thrown their weight behind Keita, known as IBK, a man who earned a reputation for firmness in crushing student protests and strikes when he was prime minister in the 1990s.
Cisse, a former finance minister, took 19 percent of the first-round vote with promises to improve education, create jobs and reform the army. "I'm proud of our people who have, in such a short time, put us on a path back to the republic and to democracy," Cisse said.
Despite being Africa's No. 3 gold producer, Mali - which is twice the size of France - is one of the world's poorest and least developed nations.
"I will vote for IBK," said Tidjane Sylla, 28, a trader in the main market in Bamako, which is a stronghold of support for Keita. "He is a man of his word. When he says no, it means no." ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ For a FACTBOX on the candidates, please click For a Chronology of the Mali conflict, click ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
RESULTS DUE MID-WEEK
The military junta which overthrew Toure agreed to hand over power to a civilian transitional administration after facing sanctions from Mali's regional neighbours and pressure from the African Union, United States and European countries.
Former colonial power France has pushed for quick elections as it pulls out its 3,000 troops and hands responsibility for security to a 12,600-strong U.N. peacekeeping mission which is gradually deploying.
Some observers had warned that rushing to elections might lead to problems but European Union election observers gave the first round a clean bill of health. About 49 percent of the 6.8 million registered voters cast a ballot, a record for Mali.
Voting cards and ballots have also been distributed in refugee camps in neighbouring Mauritania, Burkina Faso and Niger, home to some 170,000 Malians.
Many Malians hope the election can change a system of "consensus politics" under which Toure seduced political opponents with government positions and failed to undertake reforms, discrediting his government in the eyes of voters.
"I think we will see a change," said Chris Fomunyoh, senior associate for Africa at the National Democratic Institute in Washington. "The personality differences between the candidates are so great that whoever loses will create a real opposition."
Keita has captured the popular mood by avoiding outspoken criticism of the coup leaders who toppled Toure, earning the tacit blessing of the military. He has also successfully courted Mali's powerful Islamic clerics, some of whom have endorsed him.
Critics say Cisse, who condemned the coup, supports the corrupt political class, but he rejects the claim, saying he is a defender of democracy. After challenging the result of the July 28 election, alleging fraud, he promised to accept the second round's outcome. (Additional reporting by Adama Diarra; Editing by Joe Bavier and David Stamp)