Hundreds of people were killed and wounded during the protests since July, which first called for the abolition of quotas in government jobs and later the resignation of the Hasina, who had been in power since 2009.
The 76-year-old is the daughter of Sheikh Mujibur Rahman, the founding leader of Bangladesh.
In an address to the nation after meeting political party leaders, Zaman called for peace and said there would be “no need” of martial law if normalcy returns to the South Asian nation. He pledged to probe deaths of the protesters.
Hasina is said to have fled to neighboring India, and has not issued any statement yet.
Earlier, students had pushed back any possibility of a military takeover. Asif Mahmud, a key coordinator of the ongoing demonstrations, said in a social media post that students "won’t accept military takeover."