Metropolitan Magistrate Mokseda Asgar partially granted the police plea in a hearing on Wednesday after Nayan surrendered in court and sought bail.
So far, three people accused in the case have been arrested.
Court police's Inspector Abu Hashem said Nayan is the prime accused.
"After surrendering, Nayan said Tuku had accidentally shot himself. But the autopsy report suggests it's a case of murder, as the bullet had struck Tuku in the back. So, police opposed Nayan's bail appeal."
Investigation officer SI Selim Badshah had sought 10 days' remand but the magistrate granted five days rejecting Nayan's bail plea, said Hashem.
District Awami League unit's Finance Secretary Tuku was shot in his business office in front of Nagra Bhaban on Apr 24 afternoon.
He was declared dead when taken to Rajshahi Medical College Hospital.
Next day, his wife Shamsunnahar Lata lodged the murder case at local police station, accusing five people.
Source: Bangladesh's First Internet Newspaper