In a military communique put out by his office, al-Bashir declared the "end of military operations" and said all three component states in the troubled area bordering Chad were "entirely in government hands."
He called for a general amnesty throughout the region provided that all rebels surrender their weapons to police within a month, and for the organisation of a conference on "development and peace" in the Darfur area.
But al-Bashir warned: "The armed forces are prepared to dissuade all those who would threaten the security of our citizens."
Colonel Abd Allah Abd al-Karim, military spokesman for the Justice and Equality Movement (JEM) - one of the rebel groups fighting against government troops in the Darfur region - quickly denied al-Bashir's claim.
"This information is false. We still control all of our positions in the Darfur region, notably in Jabal Marrah and Jabal Moun," two mountainous districts, Abd al-Karim told AFP by telephone.
Abd al-Karim, who said he was speaking from the Jabal Marrah
area, said his movement had been observing a unilateral ceasefire for over a week for "humanitarian reasons", mainly to allow refugees to move within the region.
But he promised "military surprises in the coming days", without elaborating.
The other two rebel movements - the Sudan Liberation Movement (SLM) and the Sudan Federal Democratic Alliance (SFDA) - could not be reached for comment.
About 3000 people have been killed and another 670,000 displaced within Sudan itself by the war pitting government troops against rebels drawn mainly from the region's non-Arab minorities.
About 670,000 people have been
displaced as a result of the conflict
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.
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.
Abd al-Karim confirmed the JEM had withdrawn "two weeks ago" from those areas.
Chad has repeatedly intervened as a mediator in the crisis,
securing two ceasefires that subsequently collapsed. A third round of talks in the Chadian capital Ndjamena in December failed to produce an agreement.