Prime Minister's political assistant Rashed Khan criticized retired Colonel Oli Ahmed in a Facebook post made late on 2 August.
Khan said Oli Ahmed had made derogatory comments about his parents and had questioned his family background.
Khan said Oli Ahmed had called him an agent of India's Research and Analysis Wing or Israel's Mossad.
Khan alleged that Oli Ahmed had ties and financial dealings with Masud Karim, whom Khan described as an intelligence agent.
He challenged Oli Ahmed to state that he had no relationship with Karim.
Khan further alleged that Oli Ahmed had compromised with intelligence agencies during opposition political activity.
He claimed that Oli Ahmed had sought more seats from the BNP for Jamaat-e-Islami and later joined a Jamaat alliance.
Khan said he was the child of a worker, studied at the University of Dhaka, and had tried to take part in anti-authoritarian political activity between 2018 and 2024.
He said he would continue to address Oli Ahmed respectfully despite the dispute.
Khan ended the post by accusing Oli Ahmed of acting on behalf of Jamaat-e-Islami and using insulting language about him.
No immediate response from Oli Ahmed to the allegations was recorded.