Speaking from Libreville in Gabon on Thursday, the spokesman for the Justice and Equality Movement (JEM), Abd Allah Abd al-Karim, said rebels had retaken several towns and road links from government forces.
"We have resumed fighting to prove to the Sudanese government that the statements by its president [Umar al-Bashir] are completely false."
"We occupy the vast majority of Darfur. The access routes leading to its three capitals are under our control," he added.
Forces from JEM and the Sudan Liberation Movement (SLM) - the region's largest rebel group – are believed to have reoccupied seven towns in the region.
But the government continued to maintain it had seized control of Darfur, with its refugee commissioner visiting the Chadian capital Ndjamena to inform the authorities there of the "cessation of hostilities in Darfur".
The commissioner, Muhammad Ahmad al-Aghbash, said that the two countries were also now looking at repatriating back to Sudan refugees who fled the fighting in Darfur and sought sanctuary on the Chadian side of the border.
Around 3000 people have been killed and another 670,000 displaced within Sudan itself by the war pitting government troops and their paramilitary allies against rebels drawn mainly from the region's non-Arab minorities.
"We occupy the vast majority of Darfur. The access routes leading to its three capitals are under our control"
Abd Allah Abd al-Karim,
Another 100,000 Sudanese are estimated to have fled across the border into Chad because of the rebellion that erupted a year ago over the Darfur region's alleged economic neglect by the government.
End of mediation?
Late last month, the Sudanese army announced it had taken control of a number of districts on the border with Chad, including the divided town of Tine, sparking a fresh exodus of refugees across the frontier.
Fighting intensified after the failure of negotiations in Ndjamena in December, and Chad's president Idriss Deby announced late last month that he was going to resume mediation efforts.
Chad has repeatedly intervened as a mediator in the crisis, securing two earlier ceasefires that subsequently collapsed.
But Abd al-Karim said his group did not want any more mediation from Chad, which he accused of allowing Sudanese government forces into its territory to hit rebel positions.