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The son of Bangladesh's toppled autocratic leader thanked New Delhi on Sunday for "saving her life", accused caretaker authorities of allowing "mob rule", and warned of chaos ahead without swift elections.

Sheikh Hasina, 76, quit as prime minister on Monday after a student-led uprising and fled by helicopter to longtime ally India.

Her government was accused of widespread human rights abuses, including the extrajudicial killing of thousands of her political opponents during her 15-year tenure.

The military announced her resignation and then agreed to student demands that Nobel Peace Prize winner Muhammad Yunus, 84, lead a caretaker administration, charged with ending disorder and enacting democratic reforms.

However, Hasina's son and former government adviser, US-based Sajeeb Wazed Joy, 53, criticised the interim government as "completely powerless" and composed of "figureheads".

"Right now in Bangladesh, you have mob rule," he told AFP in an interview from Washington.

He pointed to the ouster of top officials, including the chief justice, central bank governor and police chief, following protesters' demands.

"If the mob tomorrow says, 'no, we want this person in the interim government changed', they will have to be changed," he said.

'Devolve into chaos'

Yunus has said he wants elections "within a few months", but Wazed warned of risks if they were delayed.

"It's in their best interest to hold elections… to have a return to a legitimate government that has the legitimacy of the people and true authority," he said.

"Otherwise, it's just going to devolve into chaos."

Hasina swept January elections but only after a poll denounced as neither free nor fair and boycotted by genuine rivals after a crackdown during which thousands of opposition party members were arrested.

Members of Hasina's millions-strong Awami League have gone into hiding since she fled. There have been reprisal attacks against them and party offices have been torched.

But Wazed said the party was critical to the political future of the South Asian nation of some 170 million people.

"We have tens of millions of followers; they're not going anywhere," he said.

"You're not going to be able to establish democracy in Bangladesh without the Awami League. It will never be accepted by half the people of the country at least."

Former opposition groups such as the Bangladesh Nationalist Party (BNP) are rebuilding after years of repression, the BNP holding a peaceful mass rally in Dhaka since Monday.

"It's going to be between the BNP and the Awami League," Wazed said. "We need to work together."

'Excessive force'

Wazed sought to divert blame for his mother's ouster onto others in government.

"Were mistakes made? Of course," he said. "They were made by people at the bottom, or in the chain of command… Blaming my mother for it is unfortunate."

While accepting that police officers who fired on protesters had gone too far, he argued that there was violence on both sides.

"Some of the police used excessive force but there were attacks on the police too – police members were killed as well. The violence wasn't one-sided," he said.

"And then as it escalated further, the protesters started attacking police with firearms, weapons."

More than 450 people were killed in the unrest leading up to Hasina's fall – 42 of whom were police officers, according to the national police chief.

Wazed alleged unidentified foreign forces had supported the protests, a claim for which he provided no evidence.

"I believe, at this point, it is from beyond Bangladesh," he said.

"Only an intelligence agency would have the capability of smuggling and supplying weapons to protesters."

It is not clear what Hasina will do next.

Wazed offered his "gratitude to the government of Prime Minister [Narendra] Modi for saving her life and keeping her safe".

New Delhi saw a common threat in groups Hasina viewed as rivals and crushed with brutal force, including the BNP, according to analysts.

Hasina has been hosted in a secret safe house and hasn't spoken publicly since arriving at a military airbase near New Delhi.

It isn't clear how long she will now stay in India but Wazed said there "has been no such plans as of yet" of her moving to a third country.

"My mother never wanted to leave her country – her dream is to retire there," he said, adding he spoke to her every day.

"This was going to be her last term. She's 76 years old. And so she just wants to go back home. Whether she'll be able to, we're waiting to see."