"Even if we have to go to the planet Mars to quickly resume the dialogue with the Malian government... We are ready," said Mohamed Maouloud Ould Ramadane of the Arab Movement of Azawad (MAA) yesterday after meeting the Security Council delegation.
The visiting team includes the US ambassador to the UN, Samantha Power, and the French ambassador, Gerard Araud.
They met in the capital, Bamako, with leaders of the MAA and two Tuareg armed groups, the National Movement for the Liberation of Azawad (MNLA) and the High Council for the Unity of Azawad (HCUA).
The west African country, which straddles the continent's Saharan and sub-Saharan regions, exploded into crisis in 2012 when the MNLA launched a rebellion claiming Azawad as an independent state.
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Al-Qaeda-linked Islamist groups seized on the chaos created by the rebellion and a coup in Bamako to take control of northern Mali, ruling it under a brutal vision of Islamic law until former colonial ruler France sent in troops to flush them out in January 2013.
Mali, once considered a beacon of democracy in the region, is still struggling to regain its footing.
"We are demanding a special status for Azawad, demanding autonomy," Ould Ramadane told AFP, though he added the rebels recognise "Mali's territorial integrity".
French UN Ambassador Araud said the rebel groups had shown "a willingness to move forward".
"We stated that there is a feeling of urgency because there are risks of these groups' members becoming radicalised," he said.
Malian sources said a roadmap on new talks between the government and rebels will be released soon. Araud said any new talks would be based on the previous peace deal and would take place without preconditions.