Bashir has repeatedly said he will step down at the end of his term in 2015, the Sudan Tribune reported Monday.
But Turabi, the secretary general of the Popular Congress Party, said Bashir will respond to his party's requests and will seek a new term.
"[Even] if the president is sincere about his decision to step down, his party members could go in demonstrations to discourage him from his decision," Turabi added.
Several senior officials, including Bashir's two vice presidents, suggested that the decision on the presidential candidate rests with the National Congress Party, not Bashir.
Turabi said the opposition party won't participate in the 2015 general elections unless the current regime is dismantled.