The National Movement for the Liberation of Azawad (MNLA) made the statement on its website, adding that it would respect other states’ borders.
Tuareg is one of two rebel groups to have gained ground in the area after Mali’s government was ousted.
Coup leaders took over in protest at the failure to stem the rebellion.
The declaration comes as rights group Amnesty International warned that Mali was on the brink of a major humanitarian disaster in the wake of the rebellion.
It demanded that aid agencies be given immediate access to the country after days of looting, abduction and chaos in the northern towns of Gao, Kidal and the historic city of Timbuktu.
On Thursday the MNLA rebels declared a “unilateral” ceasefire after the UN Security Council called for an end to the fighting in Mali – and after it said it had secured territory.
A statement posted on the rebel website on Friday proclaimed independence, adding it would respect existing borders with neighboring states and adhere to the UN Charter. The statement also called for recognition from the international community.
“We completely accept the role and responsibility that behoves us to secure this territory. We have ended a very important fight, that of liberation… now the biggest task commences,” rebel spokesman Mossa Ag Attaher is quoted as saying by the AFP news agency.
However, it is unclear which of several groups is actually in charge in northern Mali.
The MNLA was formed last year, partly by well-armed Tuareg fighters returning from Libya, where they had backed former leader Muammar Gaddafi.
But the UN has voiced alarm at the presence of the Ansar Dine group amid the rebel forces, which has links to al-Qaeda and wants to impose Islamic law, or Sharia, across the whole of the West African state.
Unlike the MNLA, Ansar Dine is not in favor of an independent northern state. AFP reports that Islamist rebels have begun exerting control in parts of northern Mali.
Mali has been in disarray ever since the 22 March coup enabled rebels to secure territory in the north.
People are continuing to flee the area and buses to the capital have been packed with people desperate to get out. Reports say the situation in the northern town of Gao, in rebel hands, is particularly tense.
The Algerian government also says seven members of its staff were kidnapped by unknown gunmen in Gao. The consul and six colleagues were forced to leave their diplomatic mission at gunpoint.
The Algerian government says it is doing all it can to find them.
Mali’s borders have been closed to trade, the country’s access to funds at the central bank for the region’s common currency frozen and travel bans slapped on coup leaders and their supporters.
The coup and Tuareg rebellion have exacerbated a humanitarian crisis in Mali and some neighboring countries, with aid agencies warning that 13 million people need food aid following a drought in the region.
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