The pair, who have adopted the aliases Reem and Rawan, said in a statement from their lawyer they had renounced Islam and fear the death penalty if forced to return to Saudi Arabia.
The sisters aged 20 and 18, whose representatives say they suffered violent abuse, fled to Hong Kong in September from a family holiday in Sri Lanka and were planning to fly on to Australia.
But they say they were obstructed by Saudi officials and have been living in hiding in the Chinese city for nearly six months since.
"We fled our home to ensure our safety. We hope that we can be given asylum in a country which recognises women's rights and treats them as equals," the pair said in the statement shared by prominent lawyer Michael Vidler.
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The case has emerged a month after 18-year-old Saudi woman Rahaf Mohammed al-Qunun drew global attention with her dramatic escape from an allegedly abusive family, gaining refugee status in Canada last month.
According to the lawyer's statement, they were intercepted during their stopover by unknown men who took their passports and "attempted to deceive the sisters" into boarding a flight back to Saudi Arabia.
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"We dream of being in a safe place where we can be normal young women, free from violence and oppression," the sisters said.
They tweeted Thursday, using the account @hksisters6, to say their passports had been invalidated and they feared being forced to go to the Saudi consulate in Hong Kong.
Our passports have been invalidated by the Saudi Gvt, which has prevented us from leaving and we think is an attempt to force us to go into the Saudi Consulate. We do not want to face the same fate as Mr Jamal Khashoggi.
— #HKSaudisisters (@HKsisters6) February 21, 2019
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