* France says Malian state can only return to north after talks
* Tuareg rebels want self-determination, ready for talks
* Fears of reprisals after some in north joined Islamist militants
By John Irish
PARIS, Jan 30 (Reuters) - Mali's interim government in Bamako must begin immediate talks with the country's northern population including armed groups that recognise the territorial integrity of the West African state, France said on Wednesday.
"The Malian authorities must begin without delay talks with the legitimate representatives of the northern population and non-terrorist armed groups that recognise Mali's integrity," French Foreign ministry spokesman Philippe Lalliot said.
Lalliot was speaking after French troops entered Kidal, the last major rebel-held town in the north of the country, signalling a new phase in the three-week French-led offensive to oust al Qaeda-linked militants from its former colony.
"Only a north-south dialogue will enable the return of Malian state in the north of the country," Lalliot said.
Mali President Dioncounda Traore on Wednesday said his government aimed to organise credible elections for July 31 in response to demands from major Western backers of the anti-rebel action.
Tuareg MNLA rebels who want greater autonomy for the desert north said earlier this week that they had taken control of Kidal after Islamists abandoned the town.
The MNLA launched a rebellion in northern Mali early in 2012, wresting control of the region from government forces after a military coup in March which was prompted by the government's handling of the uprising.
The Tuareg rebellion was quickly hijacked by an alliance of Islamist groups, which had initially fought alongside them but soon drove them from power in the main cities of the desert region the size of Texas, dubbed Azawad by the rebels.
"We reiterate that we are ready to talk with Bamako and to find a political solution," Moussa Ag Assarid, an MNLA spokesman in Paris, said.
"We want self-determination, but all that will be up to negotiations which will determine at what level both parties can go."
French and Malian troops retook the two Saharan trading towns of Timbuktu and Gao at the weekend virtually unopposed.
Residents reported some looting of shops in Timbuktu owned by Arabs and Tuaregs suspected of having helped the Islamists.
Malian troops have also been accused by international human rights groups of carrying out revenge killings of suspected Islamist rebels and sympathisers in retaken areas.
"Reconciling the Tuaregs with their Malian co-citizens will be extremely complicated," said Francois Heisbourg, a special adviser at the Foundation for Strategic Research, a Paris-based think-tank. "Some of these groups made the wrong choice so reconciling them in these circumstances will not be a piece of cake." (Reporting By John Irish; Editing by Jon Boyle)