Bangladesh's protest leaders said they expect members of an interim government, led by Nobel laureate Muhammad Yunus, to be finalised on Wednesday after Prime Minister Sheikh Hasina quit and fled to India following a violent crackdown on a student-led uprising.

Bangladesh's president appointed Yunus as the head of the interim government late on Tuesday, meeting a key demand of students, and said the remaining members need to be finalised soon to overcome the current crisis, according to a statement from his office.

The interim government will fill a power vacuum left after Bangladesh's army chief announced Hasina's resignation in a televised address on Monday that followed weeks of deadly violence that ripped through the country, killing about 300 people and injuring thousands.

The interim government is also expected to hold elections soon after taking charge. Yunus is expected to arrive in Dhaka on Thursday after a medical procedure in Paris, a spokesperson said.

Nahid Islam, one of the main leaders of the student movement, told reporters after President Mohammed Shahabuddin's announcement that students have recommended 10-15 members for the interim government in an initial list they shared with the president.

Islam said he expects interim government members to be finalised in 24 hours starting from late Tuesday evening. The students' recommendations for the government include civil society members and also student representatives, Islam said.

Shahabuddin has also recommended that a veteran of Bangladesh's 1971 independence war from Pakistan should be nominated to the interim government.

The movement that toppled Hasina rose out of demonstrations against public sector job quotas for families of veterans of the war, seen by critics as a means to reserve jobs for allies of the ruling party. Hasina landed in New Delhi on Monday and is staying at a safe house on the outskirts of the capital.