Murad stepped down on Tuesday, ordered by Prime Minister Sheikh Hasina.
The Awami League, Murad’s party, discussed whether legal action should be taken against him. The BNP, meanwhile, has called for his arrest.
Murad, 47, a doctor by training, has been in the eye of a social media storm for his offensive remarks on former prime minister Khaleda Zia's granddaughter.
Amid the furore, an audio clip of a telephone conversation began to circulate on Facebook. In the audio record purported to have his voice, Murad was heard using a stream of obscene words and threatening to drag an actress into a five-star hotel and rape her.
Actress Mahiya Mahi later took to social media and confirmed that she was the other party in the conversation with Murad.
Asked whether Murad should be questioned over the remarks caught on audio, AKM Hafiz Akhtar, additional commissioner of the Dhaka Metropolitan Police said detectives would investigate if a complaint was filed.
“If someone files a complaint or a case against him, we will look into it. But we are not considering it ourselves for the moment.”