* Fighting threatens to plunge desert north back into war
* Rebels repulsed army's attempt to take northern stronghold
* Separatists say they will respect calls for ceasefire (Adds comment from Security Council, rebels, government)
By Tiemoko Diallo
BAMAKO, May 22 (Reuters) - Tuareg separatists said on Thursday they had seized 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, MINUSMA, or fled south.
"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.
After the fighting, MINUSMA gave shelter to 62 government soldiers at its camp in Kidal and 290 at Aguelhok. In the last few days it has treated 20 wounded, of whom two were in a serious condition, the U.N. mission said in a statement.
"Grave violations of human rights were committed during the fighting in Kidal," it 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.
"MINUSMA is working in coordination with key international partners ... to develop a potential series of measures to formalise the ceasefire in the country and encourage the parties to bring about a return to the political process," said U.N. spokesman Stephane Dujarric.
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 resolve the cycle of Tuareg rebellions in the north.
Mali was plunged into chaos in 2012 after Tuareg independence fighters teamed up with groups teamed up with groups linked to al Qaeda to seize the north following a coup in the capital.
When they were sidelined by the better-equipped Islamists, the separatists broke with their allies. A French-led military operation then drove the Islamists back last year.
Neighbouring Burkina Faso's foreign minister, Djibril Bassolé, who has served as a mediator in Mali, 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 the conflict prevention think tank 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."
The ease with which the MNLA repelled 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 it may now be renewing its alliance with Islamist groups.
Four rebel soldiers died in the fighting and eight were wounded, Moussa Ag Assarid of the MLNA told Reuters. (Additional reporting by Adama Diarra in Bamako, John Irish in Paris, Bate Felix in Dakar and Joe Bavier in Abidjan; Writing by Matthew Mpoke Bigg; Editing by Kevin Liffey)