* Mali army, Tuareg rebels clash over Kidal
* Rebels say control towns, seized Mali military camp
* Army says launched offensive after reinforcement
* Former colonial power France sending more troops (Adds government statement)
By Adama Diarra and Tiemoko Diallo
BAMAKO, May 21 (Reuters) - Tuareg separatists repulsed an attempt by Mali's army to take control of their stronghold of Kidal and seized another northern town on Wednesday, setbacks that could potentially embarrass President Ibrahim Boubacar Keita's government.
Malian troops launched the offensive to retake control of Kidal after a clash over the weekend, while Prime Minister Moussa Mara was visiting. At least eight soldiers and eight civilians were killed. Government forces then reinforced their positions.
The renewed fighting threatens efforts to find a peaceful solution to the long cycle of Tuareg rebellions in Mali's desert north.
The last rebellion in 2012 threw Mali into chaos when al Qaeda-linked Islamists hijacked the uprising and seized control of the country's north. A French-led military operation, known as Serval, drove them back last year.
The clash also upsets plans by France and West African countries to combat Islamist militants operating in the region where they are regarded as a threat to trade and foreign investment, including oil and gas installations in North Africa.
In a statement, U.N. Secretary-General Ban Ki-moon called for an immediate cessation of the fighting and the establishment of a ceasefire in the sprawling West African country.
Attaye Ag Mohamed, an official with the Tuareg rebel group MNLA in Kidal, told Reuters by telephone that the group was in control of the northern stronghold town and had also taken control of Menaka, another northern town.
"All of Kidal including the Malian Military Camp 1, the regional governor's office and the Kidal fortress are in our control," Mohamed said, adding that several Malian army soldiers had been killed, wounded or captured.
"On our side, two fighters were killed and eight others were wounded," he said.
Two Kidal residents told Reuters that over a dozen bodies of dead Malian troops could be seen at the camp while the rebels were patrolling the streets.
The Malian government said in a statement on national radio earlier on Wednesday that its troops had launched the operations to secure and take control of Kidal.
The government said late on Wednesday that while its troops initially had an upper hand, they were weakened by coordination and intelligence problems and had to withdraw under fire from the rebels.
"The president has called for an immediate ceasefire," Mali government spokesman Mahamane Baby, said on state television, adding that an investigation had been launched.
A Bamako-based diplomat told Reuters that the Malian army offensive had been beaten back, making it look like an ill-timed attack that could embarrass the government.
Another diplomat told Reuters several wounded Malian soldiers have evacuated by the U.N. peace keeping mission MINUSMA and French troops.
"This is embarrassing, but the Malians are in their country and are free to do as they see fit," said another western diplomat.
Gerard Araud, French ambassador to the UN, said in tweet that the Malian government assumed its responsibilities. "It did not inform neither MINUSMA nor the French Serval. It is a Malian affair."
The government agreed with a number of armed groups to hold talks over autonomy last year. The groups included the MNLA, which broke with the Islamists before the French offensive.
It was unclear which groups took part in the fighting on Wednesday, but a diplomat said it was not just the MNLA. He added that some fighters with ties to Islamist militant groups may have also taken part in the battle.
The flare-up in a trouble spot many had hoped was now under control occurred as West African nations and their international partners have been redoubling efforts to contain Islamist insurgents such as Boko Haram in Nigeria.
France, in particular, had hoped to move troops from Mali and other bases to target Islamist groups operating between southern Libya, northern Chad and northern Niger, fearing the fighters could use the region as a base for wider attacks.
However, French officials said on Tuesday the redeployment, expected to involve around 3,000 troops, would be delayed in light of the situation in northern Mali.
And on Wednesday, an army spokesman said France would reinforce its presence in Mali with 100 more soldiers, bringing total deployment to its former colony to some 1,700. (Additional reporting by Bate Felix, Joe Bavier and David Lewis in Dakar and John Irish and Marine Pennetier in Paris; Writing by Joe Bavier and Bate Felix; Editing by Mark Heinrich and Eric Walsh)