Thai immigration authorities said Qunun was refused entry because she did not have the proper documents.
A statement issued Monday by the office of the U.N. High Commissioner for refugees said it sought to assess 18-year-old Rahaf Mohammed Alqunun's "need for worldwide refugee protection and find an immediate solution for her situation".
A video in which she is heard talking to someone asking for the United Nations has been viewed more than 60,000 times.
Alqunun told Human Rights Watch she was fleeing abuse from her family, including beatings and death threats from her male relatives who forced her to remain in her room for six months for cutting her hair.
"If she prefers to travel to Australia, we will coordinate with the (Australian) embassy for her".
Thailand's immigration police chief says the father of the young Saudi woman who is trapped in Bangkok after being stopped en route to seeking asylum in Australia is supposed to arrive in Thailand on Monday night. She has a valid Australian visa.
Alqunun's ordeal began when she fled from her family while in Kuwait and boarded a flight to Thailand, apparently taking advantage of being away from Saudi Arabia's restrictions on women who can not travel overseas without a man's consent.
Rahaf Mohammed Alqunun, 18, was on holiday with her family in Kuwait when she fled to Bangkok, hoping to make it onward to Australia to seek asylum.
"I'm afraid, my family WILL kill me", she said on Twitter, where she shared her photograph, passport details and name, saying she had "nothing to lose". However, she had not applied to enter Thailand because her passport was taken, along with her plane ticket to Australia. "After that he took my passport".
"They wont let me drive or travel". In extreme cases, they may even kill a daughter or female relative who "dishonors" the family.
The Saudi foreign ministry said in a tweet that its embassy was in touch with the teen's father and the Thai government, but its diplomats had not met or communicated with her.
Surachate also acknowledged for the first time Saudi embassy had alerted Thai authorities to Qunun's arrival.
Rahaf Mohammed al-Qunun has been at Bangkok's worldwide airport since Saturday when she arrived from Kuwait.
Al-Qunun may be at serious risk of harm if returned to her family. "I'm not leaving my room until I see UNHCR", she said. A spokesman for Kuwait Airways said he had no information about the case, Reuters reported.
"In the event when we suspect that someone might be illegally detained, we request for the court to call the relevant authorities (in) for questioning", said Ms Bergman.
Human Rights Watch has documented that under Saudi Arabia's male guardianship system, adult women must obtain permission from a male guardian to travel overseas, marry, or be released from prison, and may be required to provide a guardian's consent to work or get health care.
The ultra-conservative Saudi kingdom has always been criticised for imposing some of the world's toughest restrictions on women.
Thai lawyers, working pro-bono, on Monday filed an injunction against deporting the young woman, and charged that she had been wrongfully detained. "They threaten to kill me and prevent me from continuing my education", she said.
An immigration official later said she would not be forced to leave Thailand because of concerns for her well-being.
Immigration police chief Surachate contradicted parts of Alqunun's story, including her claim that she had an Australian visa. Her fate on arriving back in Saudi Arabia remains unknown.
She had been holed up in a Bangkok hotel room, after being stopped by Saudi Arabian diplomatic staff who claimed she did not have the correct documentation.
While the Saudi Embassy in Thailand denied that Saudi authorities were involved in attempts to stop Alqunun from traveling to Australia, the kingdom has in the past forcibly returned its citizens home.