But law firm Vidler & Co Solicitors, who is representing the pair, said upon their arrival at Hong Kong airport on September 6, the women discovered their connecting flight to Melbourne was cancelled.
The women allege they were then obstructed by Saudi officials and have been living in hiding in Hong Kong since.
Their lawyers say the woman had been forced to change locations 13 times for fear of their safety after police reportedly tried to take them to meet male relatives and Saudi officials.
«Upon their immediate arrival in Hong Kong, Reem and Rawan were approached by two males,» Vidler & Co Solicitors said in a statement late on Thursday.
The sisters later learned one of the two men was Saudi Arabia’s consul general in Hong Kong, the solicitors said.
«Neither identified themselves to the sisters. Believing the men were assisting them, the sisters followed the men through a security checkpoint,» the statement said.
«The airline has since confirmed that the men were acting ‘solely at the request of the Royal Consulate General of Saudi Arabia in Hong Kong’.»
The law firm also alleges a Sri Lankan Airlines employee briefly snatched their passports, and only handed them back when the sister threatened to summon police.
«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 their lawyer Michael Vidler.
«We dream of being in a safe place where we can be normal young women, free from violence and oppression.»
The sisters’ case comes weeks after 18-year-old Saudi woman Rahaf Mohammed al-Qunun sparked global attention when she was detained by Saudi authorities at Bangkok airport, from where she had planned to travel to Australia to seek asylum.
She had barricaded herself in her hotel room at the airport after claiming a Saudi official confiscated her passport and planned to forcibly return her to her departure point of Kuwait and onwards to her family in Saudi Arabia, whom she feared would kill her.
She gained refugee status in Canada last month.
Mr Vidler told American news network CNN on Thursday he believed the sisters were the subject of an attempted kidnapping.
«The Saudi Consulate was actively trying to deceive them,» he said.
Rawan also told CNN the sisters saw no future for themselves in Saudi Arabia.
«It’s slavery, because whatever the woman will do it’s the business of the male,» she told the network.
«When I was growing up I saw my brothers do whatever they want, have whatever they want. But for me, I should be a good girl, a good woman, to marry someone, my cousin, because I should not even dream to choose my husband, to choose my partner.»
Representatives for the women also claim the sisters made a report to Hong Kong police about the events at the airport and their concerns for their safety.
The Department of Home Affairs and Saudi Consulate in Hong Kong have been contacted for comment.