The Saudi embassy in Bangkok has issued a statement denying its role in holding her, and said Thai authorities stopped her for "violating the law".
"She's desperately fearful of her family, including her father who is a senior government official, and given Saudi Arabia's long track record of looking the other way in so-called honour violence incidents, her worry that she could be killed if returned cannot be ignored", he added.
Ms Qunun told AFP she feared that she would be killed if she is returned to Saudi Arabia.
"My life is in danger". The Australian Embassy said it had no immediate comment.
Repeating her desire to leave Thailand for another country where she can seek asylum, Alqunun said, "But at least I feel [safe] now under UNHCR protection with the agreement of Thailand authorities". "She is 18 years old, she has an Australian visa, and she has the right to travel where she wishes and no government should interfere in that".
"They said we do not have enough evidence", she told AFP, adding she planned to appeal.
"My brothers and family and the Saudi embassy will be waiting for me in Kuwait", Qunun said by text and voice message from the hotel on Sunday. "Thailand is a land of smiles".
Mr Surachate said he would meet Saudi diplomats on Tuesday to clarify Thailand's decision. Requests for asylum can not be made in Thailand as it is not a signatory to global conventions on refugees, nor does Bangkok recognize the legal status of those entering the kingdom.
She was on her way to Australia but has been stopped in Bangkok by Thai authorities due to not having a return flight.
U.N. representatives have now met with Al-Qunun, according to Melissa Fleming, the head of communications and chief spokesperson for the United Nations High Commissioner for Refugees.
How did the stand-off start?
Rahaf Mohammed Al-Qunun, whose situation has gone viral via her Twitter feed, told Human Rights Watch that she arrived at the airport on January 5 from Kuwait, and that her passport was seized, preventing her from travelling to Australia.
"I can't escape the airport", she said in the live video. Al-Qunun said however that she resides in Saudi Arabia, posting a picture of her university identification card.
Surachate had told reporters earlier Monday Alqunun was stopped by immigration because Saudi officials had contacted them to say she had fled her family.
Thai Major General Surachate Hakparn said the teenager had indicated that she remains unwilling to go back home. She also gave a friend, Noura, access to her Twitter account, saying it was in case anything should happen to her. "I can't study and work in my country, so I want to be free and study and work as I want", she explained.
The Saudi embassy in Bangkok said in a Twitter statement it had not impounded Al-Qunun's passport, adding it doesn't have the authority to stop her at the airport or anywhere else. Qunun, however, told AFP that she was only travelling in the Gulf state. "The Liberal Government must act swiftly and bring her here to safety".
Why are there fears for her welfare?
'She's in Thailand now, ' Surachate Hakparn, the nation's immigration chief, said in a briefing Monday afternoon at the Suvarnabhumi Airport.
Freedom of religion is not legally protected in the kingdom, and people who convert to another religion from Islam risk being charged with apostasy - or abandoning their religious beliefs. These restrictions last from birth until death, as the Saudi state views women as permanent legal minors.
Hours later, al-Qunun sent out a video in which she said she will barricade herself in her hotel room until she is allowed to see UNCHR officials to apply for asylum. Saudi Arabia denies its officials were involved in any way. She said she intends to seek asylum there.
Alqunun is "incredibly courageous and fearless, and she's exhausted, but she is prepared to fight to the end", Robertson said.
Saudi women like Dina Ali Lasloom who was stopped in the Philippines, two Saudi sisters who fled to Turkey, and now Rafah Alqunun in Thailand have all used Twitter and social media to raise awareness of their plight and ask for help.