Begum, who gave birth this month in a refugee camp, has said she wants to come home but the British government has decided to revoke her citizenship, calling her a security threat.
The 19-year-old's father Ahmed Ali said that while his daughter had made mistakes, Britain was duty-bound to let her return.
"The British government should take her back because she is a British citizen," said Ali, who has been following Begum's plight from a remote village in northeastern Bangladesh.
"If she has committed any crime, they should bring her back to London, to her country, and punish her there."
Begum left the UK for Syria with two school friends in 2015, when she was just 15.
Public sentiment hardened against Begum after she showed little remorse about IS attacks in media interviews from the camp in eastern Syria, where she arrived after fleeing fighting between the terror group and US-backed forces.
Ali, 60, said comments he had made to a London newspaper saying he backed UK interior minister Sajid Javid's decision to strip Begum of her nationality had been "misinterpreted".
"I don't think that (to revoke Begum's citizenship) was a right thing to do," he said. "To err is human. You and I can both can make a mistake. It is OK to commit an error, all humans do that. One feels sad if a child commits a mistake," he told AFP.
Islamic State teen 'shocked' after UK revokes her citizenship
Ali, who lives with his second wife in the village of Daorai in Sunamganj district, said he felt sorry for his daughter and believed she may have been brainwashed into joining IS.
"It was certainly a mistake to go to IS. Perhaps it was because she was a child. She may not have gone there (Syria) willingly. She may have been ill-advised by other people," he said.
Ahmed last saw his daughter in Britain just two months before she fled to Syria with Kadiza Sultana and Amira Abase in March 2015.
He says she did not show any sign of having been radicalised. "I did not see any such thing at all."
He also highlighted how the Bangladesh government has declared that Begum would not be allowed into the country.
The British government reportedly believes that Begum was entitled to claim Bangladesh citizenship, though this is disputed by the South Asian country.
"She can't come to Bangladesh since she is not a citizen of this country," he said.
Tasnime Akunjee, a lawyer for Begum's family, earlier said the teenager was born in Britain and had never had a Bangladeshi passport.
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