* Six rebel groups in Algiers for talks with Mali government
* "We must build a new Mali" - rebel negotiator
* Rebels divided among themselves, distrust government (Adds remarks from minister, rebel negotiator)
By Patrick Markey
ALGIERS, July 16 (Reuters) - Mali's government and rebels held peace talks in Algiers on Wednesday in a bid to end decades of uprisings by northern Tuareg tribes after an exchange of prisoners helped get the negotiations started.
Mali's vast desert north - called Azawad by the rebels - has risen up four times since independence from France in 1960, most recently last year, when French forces intervened to drive back Islamists who had taken advantage of a Tuareg-led rebellion.
The talks are the first since fighting in the Tuareg stronghold of Kidal killed around 50 Malian soldiers in May. The light-skinned Tuaregs and Arabs perennially accuse black African governments in the capital Bamako of excluding them from power.
France, Mali's northern neighbour Algeria and the West Africa regional bloc ECOWAS are all pushing for talks despite deep distrust between Bamako and rebels, and among the different separatist groups.
The negotiations, which include representatives of the United Nations, European Union and the African Union, aim to lay out a roadmap for a broad peace deal in the West African nation.
"There is a historic responsibility together to find peace at last," Mali's Foreign Minister Abdoulaye Diop said at the opening of the talks in a hotel in the Algerian capital.
Algeria's government said it had helped to broker the prison swap - 45 civilians and troops from the government in exchange for 42 members and sympathisers of rebel movements.
Three main rebel groups - the Tuareg MNLA and High Council for the Unity of Azawad (HCUA), as well as the Arab Movement of Azawad (MAA) - have sought to unify their positions, but there are divisions within the different Tuareg factions and between Tuareg and Arab separatist groups.
"We are here to construct a roadmap and launch a profound dialogue," rebel negotiator Mahamadou Djeri Maiga told reporters. "We have accepted the integrity of Mali, we are also for a secure state, we must build a new Mali."
DIVISIONS AMONG REBELS
President Ibrahim Boubacar Keita was elected last year partly for his reputation for taking a firm stand against previous uprisings, and is under pressure from the more densely populated south not to give in to rebel demands.
But the army's inability to defeat rebel forces has severely undermined Bamako's position. The U.N. Security Council has warned that failure to hold inclusive talks could further radicalise rebel fighters.
Talks advanced in June after a preliminary accord. But analysts said the rebels had to make concrete, coherent proposals and overcome splits in their ranks.
Andrew Lebovich, a New York-based researcher and analyst on the Sahel region, said an agreement was possible in Algiers, but a deal signed outside Mali would not necessarily carry weight with the diverse and fragmented fighters on the ground.
"An agreement is only one step in a much longer process, and a deal itself will not guarantee or even potentially lead to a resolution to the various conflicts in northern Mali," he said.
French troops were dispatched to Mali last year to force back al-Qaeda linked Islamist militants who occupied swathes of northern Mali.
Isolated attacks by Islamists have continued in northern Mali despite the presence of thousands of French and U.N. peacekeepers. A French soldier was killed this week in the first suicide attack on French forces in Mali.
Paris is in the process of reorganising its deployment in the region, with its 1,700 soldiers in Mali being folded into a broader, Sahel-wide counter terrorism force. (Additional reporting by Hamid Ould Ahmed; Editing by Kevin Liffey and Andrew Heavens)