Her urgent pleas for help over Twitter from an airport hotel room garnered tens of thousands of followers and the attention of the UN's refugee agency, the UN High Commissioner for Refugees.
The story of the 18-year-old Saudi women who fled her family seeking asylum to reclaim her rights has been the talk of the town for the past few days with the trending hashtag 'Save Rahaf' on Twitter.
On Monday she was allowed to leave the airport in the care of the UN's refugee agency.
It also said the embassy had made contact with her father, a senior regional government official in the kingdom, "to inform him on her situation".
A British woman launched an online petition calling on Foreign Secretary Jeremy Hunt to grant al-Qunun asylum and issue her an emergency travel document.
A Saudi woman's ongoing bid to flee her country via Thailand this week threw the kingdom's male guardianship system into the worldwide limelight, setting in motion a showdown between Saudi Arabia's restrictions on women and the United Nations' asylum process.
"The government will be making no further comment on this matter", it said.
He said he would talk to the United Nations refugee agency about a potential meeting between the family members. 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.
"It's extremely concerning if it is the case that the visa has been canceled", she told The Associated Press, adding that Australia should allow Alqunun entry in any case. She also noted that her passport had been returned to her after it was confiscated on Sunday.More news: Editor's Corner-With Samsung deal, Apple is finally dropping video distribution hints
"The Department of Home Affairs will consider this referral in the usual way, as it does with all UNHCR referrals", a spokesperson said. "I only gave her my business card in case she needed anything or had any questions", he said.
"We have no idea what he is going to do. whether he will try to find out where she is and go harass her".
Alqunun told The New York Times that she started planning an escape when she was 16.
A statement from the Saudi Embassy describes al-Qunun's case as a "family affair", and that the kingdom did not demand her deportation to Saudi Arabia.
After being informed by immigration that she would be placed on a flight back to Kuwait, the young woman barricaded herself in her airport hotel room and began launching a barrage of appeals to the Twittersphere.
Gen. Surachate Hakparn said that Alqunun's father and brother arrived together in Bangkok on Tuesday but Alqunun refused to meet them.
In Saudi Arabia, women are forbidden from travelling without a male escort, whether they be a father, uncle, husband, brother, or son.
"Only she can make that choice, she's an adult woman who can make her own decisions!"
Thai officials had tried to force her take a flight to Kuwait, Saudi Arabia scheduled for the morning of January 7.
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.