Bangladesh Prime Minister Sheikh Hasina on Monday resigned and fled the country in the wake of hundreds of deaths in a crackdown on demonstrations that began as protests against job quotas and swelled into a movement demanding her downfall.

Protesters stormed the grounds of the presidential residence while elsewhere in Dhaka protestors climbed atop a statue of Hasina's father, state founder Sheikh Mujibur Rahman, and began chiselling away at the head with an axe.

The flight into exile ended a 15-year second stint in power for Hasina, who has ruled for 20 of the last 30 years as leader of the political movement inherited from her father, assassinated with most of his family in a 1975 coup.

Army chief General Waker-Uz-Zaman announced Hasina's resignation in a televised address to the nation and said an interim government would be formed. He called for peace and promised justice for those killed in weeks of unrest.

"I am taking full responsibility," the general said, dressed in military fatigues and cap, although it was not immediately clear if he would head a caretaker government.

"The country has suffered a lot, the economy has been hit, many people have been killed - it is time to stop the violence," he said.

"I hope after my speech, the situation will improve."

The 58-year-old said he had held talks with leaders of major political parties - excluding Hasina's long-ruling Awami League - and would soon meet President Mohammed Shahabuddin to discuss the way ahead.