The multinational African Union swiftly rejected the declaration by the rebels' National Movement for the Liberation of Azawad, calling it null and void.
Mali's former colonial power, France, also refused to recognize the declaration.
The rebel organization, known as MNLA, has accelerated its battle for control of northern Mali since rebel soldiers carried out a coup that toppled the democratically elected government two weeks ago.
At the time, coup leaders accused the government of failing to deal with the rebels, led by ethnic Tuaregs, and their Islamist supporters, who want to enforce sharia law across Mali.
On its website, MNLA cites atrocities and more than 50 years of bad governance for asserting the right to declare Azawad an independent state, separate from Mali.
Recalling the massacres, atrocities and humiliation, dispossession and genocide of 1963, 1990, 2006, 2010 and 2012, which targeted only the people of Azawad until 1 April 2012, the statement read.
Speaking to Agence France-Presse, rebel spokesman Mossa Ag said: 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.
Elsewhere, Amnesty International warned Friday that Mali is on the verge of a major humanitarian disaster.
The human-rights group demanded access to the country, especially the northern towns of Gao, Kidal and Timbuktu, which have seen widespread looting and abductions after being taken by rebel forces.
The move is a further setback for coup leaders, who have become increasingly isolated by the international community.
Earlier this week, regional body Ecowas imposed diplomatic and economic sanctions on Mali after the coup leaders failed to step down.
The sanctions include suspension of Mali's membership in Ecowas, a freeze on coup leaders' assets and closure of landlocked Mali's borders with Ecowas neighbors.
The Tuaregs began their battle for independence in January began, demanding autonomy from Mali's capital, Bamako.