Rahaf, a Saudi national, fled her family last week.
As for providing security in light of Khashoggi's murder in the Saudi consulate in Istanbul, he said "that's the Thai government's job and I hope that's being looked into". But the Saudi Embassy in Bangkok claims it is only "monitoring her situation".
Greens senator Sarah Hanson-Young, the first Australian MP to call for Australia to provide refuge to Ms al-Qunun, said it was "time to bring this courageous young woman to Australia to start her life as a free woman". She alleged that she was being subjected to physical and psychological abuse by her family.
Fleeing her family and "saved" from deportation following social media outcry, a young Saudi woman is one step closer to receiving asylum in Australia, while local officials say she won't get "special treatment". The said both countries had the same aim, the safety of the girl, with the diplomat saying that he was satisfied with Thailand's decisions on the matter.
"The father is now here in Thailand and that's a source of concern", Phil Robertson, Human Rights Watch's deputy director for Asia, told Reuters. "They will take me to Saudi Arabia and my father will kill me because he is so angry", she said. Surachate said that UNHCR, "will take five days to consider her status" and another five days to arrange for travel.
"Everybody was watching. When social media works, this is what happens", said Mr Phil Robertson, deputy Asia director for Human Rights Watch, of the worldwide outcry.
The 18-year-old was stopped by officials in Thailand who confiscated her passport. She was referred to Australia for resettlement.
Alqunun's father, a Saudi government official, and brother arrived in Bangkok on the evening of January 8 and immediately demanded to see her.
The ultra-conservative kingdom has some of the world's toughest restrictions on women, including a guardianship system that allows male family members to make decisions on behalf of female relatives.
Fearing for her life should Thai authorities decide to repatriate her, she barricaded herself in her hotel room at Suvarnabhumi airport in Bangkok and demanded United Nations protection before she could leave.
Alqunun said her male guardian had reported her for travelling "without his permission".
"She does not wish to go back and we will not force her".
A young Saudi woman is asking for Canada's help after tweets about her efforts to flee abuse and seek asylum overseas put her in the global spotlight.
Thai immigration officials had initially said she should return to Kuwait.
Friends of Saudi woman Ms Alqunun claim she was nearly forced onto a flight from Thailand back to Kuwait despite seeking asylum in Australia.
Global pressure has mounted on Thai authorities to keep Alqunun safe and to ensure she isn't forcibly returned to the Saudi kingdom, which has been subject to worldwide condemnation over the killing of Washington Post writer Jamal Khashoggi at a Saudi consulate in Turkey.