Speaking to Aljazeera's correspondent in Khartoum, al-Bashir described the Darfur rebels' demands as "surprising even to the province's residents".
The signing of the peace agreement "should have been concluded a long time ago", he said.
Among their appeals, explained al-Bashir, are the separation of religion and state.
"We have completely surpassed this issue, even with the non-Muslim majority southern areas.
"It is strange that they are talking on behalf of Darfur residents and demanding the separation of religion and state."
Still in conflict
The president added that it "was clear they have no plan as they are not a genuine movement".
The evidence, continued al-Bashir, is that "Europeans have tried to create a movement out of these armed groups in Darfur, to train and teach them".
All attempts, however, to create a movement with objectives have failed, he said.
Sudan is to have a new constitution on Saturday as it enters a six-year interim period aimed at giving the strife-torn country a fresh start and sealing a peace deal that ended Africa's longest civil war.
However, even after the historic peace agreement that was signed in Kenya on 9 January between the Khartoum government and southern rebels, Sudan remains mired in conflict in the Darfur region and in the volatile east.