But she was intercepted by Thai authorities, who initially wanted to send her back to her family.al-Qunun says her family consider her a "slave", and would kill her if she were sent back, as punishment for renouncing Islam.
She escaped from them in Kuwait on Saturday by boarding a flight to Bangkok, intending to fly from here to Australia and apply for asylum. She had hoped to travel to Australia where she has friends before she was detained at the Bangkok airport this past weekend and threatened with deportation.
Photos released on Monday night by immigration police showed the teenager with Thai and United Nations officials after she left the airport transit hotel room where she had been holed up over the weekend.
The department said it would "consider this referral in the usual way, as it does with all UNHCR referrals".
"The government has made representations to the Thai government and the Bangkok office of the UNHCR about its serious concerns on this matter and the need for Ms Alqunun's claim to be assessed expeditiously".
Al-Qunun's father and brother arrived in Thailand but she refused to see them.
In an interview with Saudi-owned TV channel Khalijia, the embassy official said that the woman's father contacted the diplomatic mission for "help" bringing her back. "I'm not going to open the door I want United Nations", one later tweet from her account said.
A government source toldThe Australian Ms Alqunun would be refused entry to Australia on a tourist visa because it's not her real reason for entering the country.
The father, who name has not been released, is a governor in Saudi Arabia, Lt. Gen. Surachate Hakparn said. The Guardian confirmed on Monday Qunun had a valid three-month tourist visa for Australia, issued to her Saudi passport. "What's important is get her safe so Australia really needs to move quickly to get her out of Thailand".
"She is now under the sovereignty of Thailand; no-one and no embassy can force her to go anywhere", he said. On Twitter, she has expressed fear of such a meeting.
Amnesty International's Middle East director of campaigns Samah Hadid said Rahaf's story "became an inspiration to millions worldwide", but added that Thailand has often "breached their responsibilities" to asylum seekers and refugees.
On 6 January, Rahaf Mohammed Alqunun - an 18-year-old Saudi Arabian woman - began sending messages on Twitter.
Qunun has since tweeted that she felt safe "under UNHCR protection with the agreement of Thailand authorities." . "We are both concerned for Miss Rahaf's safety and well-being", Surachate said.
In 2017, Dina Lasloom triggered an online firestorm when she was stopped en route to Australia where she planned to seek asylum.
Ms Mohammed al-Qunun's twitter account later quoted a Saudi diplomat in Bangkok saying it would have been better to take her phone than her passport.
The latest incident comes against the backdrop of intense scrutiny on Saudi Arabia over the shocking murder of Saudi journalist Jamal Khashoggi a year ago, which has renewed criticism of the kingdom's rights record.