* Fighting threatens to plunge desert north back into war
* Rebels repulsed army's attempt to take northern stronghold
* Separatists say will respect calls for ceasefire (Adds quotes, background)
BAMAKO, May 22 (Reuters) - Tuareg separatists said on Thursday they had seized control of several towns in northern Mali after routing government forces in fighting that threatens to plunge the desert north back into war, but said they would respect calls for a ceasefire.
The army had launched an offensive to retake control of the separatist stronghold of Kidal after clashes erupted while Prime Minister Moussa Mara was visiting the town on Saturday.
Tuareg separatists repulsed the attempt on Wednesday and on Thursday said they had taken more northern towns without a fight after government troops either abandoned their positions and sought refuge at the camps of the U.N. peacekeeping mission or fled south. Malian government officials were not immediately available for comment.
"We now control Anefis, Aguelhok, Tessalit, Menaka, Ansongo, Anderamboukane and Lere," Attaye Ag Mohamed, an official with the Tuareg National Movement for the Liberation of Azawad (MNLA), told Reuters by telephone from Kidal.
"We are going to hold our positions. We will heed the call from the international community which has asked us to cease fire. We also note that the Malian government has called for an immediate ceasefire," Attaye said.
U.N. Secretary-General Ban Ki-moon and the French government have called for an immediate cessation of fighting and the resumption of dialogue.
Mali's government issued a statement on Wednesday ordering an immediate ceasefire. It said that while its troops initially held the upper hand, they were weakened by coordination and intelligence problems.
A parliamentarian from the region, Algabass Ag Intallah, said Malian troops had pulled out of several towns and a Malian military source said the army was withdrawing from areas where it was outnumbered.
The military failure is a setback for President Ibrahim Boubacar Keita's government and threatens to sink a struggling process to find a solution to the long cycle of Tuareg rebellions in the north.
In the latest rebellion, Mali was plunged into chaos in 2012 after al Qaeda-linked groups teamed up with Tuareg independence fighters to seize the north following a military coup in the capital Bamako.
Later sidelined by the better equipped Islamists, the separatists officially broke with their erstwhile allies before a French-led military operation drove the Islamists back last year.
Neighbouring Burkina Faso's Foreign Minister Djibril Bassolé, who has served as a regional mediator in Mali's crisis, told French radio RFI: "There is a danger that the same phenomenon as in 2012 can happen again."
Rinaldo Depagne, West African programmes director at conflict prevention think-tank the International Crisis Group, said: "It's not only that (Keita) lost part of the north, he's lost part of his authority in the south. IBK (Keita) will be forced to make concessions now, but making concessions will harm his political base in the south."
The MNLA's ease in repelling government forces, some of whom were trained and equipped by the European Union as part of efforts to rebuild the army, has raised concerns that the MNLA may be renewing its alliance with its former Islamist allies.
It was unclear which groups took part in the fighting on Wednesday, but one diplomat said the MNLA was not acting alone.
The MNLA's Attaye denied that any Islamist fighters took part in the fighting.
So far French and U.N. forces in Mali have refrained from intervening in the clashes.
"For the MNLA, the big mistake would be to be too closely identified with these Islamist groups, to be seen as terrorists. Then you could see the intervention of the international community," Depagne said. (Additional reporting by John Irish in Paris, Bate Felix in Dakar and Joe Bavier in Abidjan, Writing by Bate Felix; Editing by Janet Lawrence)