Thai officials met with counterparts from the Kingdom on Tuesday and Maj Gen Surachate Hakparn, Thailand's immigration police chief, said that Saudi officials said they were satisfied with the handling of the case.
The young woman has said she was fleeing from Saudi Arabia to Australia but was stopped en route by Thai and Saudi officials.
Rahaf Alqunun arrived in Bangkok global airport on a flight from Kuwait on Tuesday after running away from her family who she says are abusive.
Thai police say a Saudi woman who fled her family to seek asylum overseas has refused to meet with her father in Thailand.
Australia says it is considering granting a Saudi who fled from her family refugee resettlement based on referral by the United Nations.
"The UNHCR has referred Ms Rahaf Mohammed Al-Qunun to Australia for consideration for refugee resettlement", the Australia Department of Home Affairs told NPR in a statement, referring to the office of the U.N. High Commissioner for Refugees.
"The claims made by Ms Al-Qunun that she may be harmed if returned to Saudi Arabia are deeply concerning", a Department of Foreign Affairs spokesman said.
Although Canadian officials said diplomats routinely raise human rights issues with their Saudi counterparts, the Saudi government reacted strongly to the public appeal and retaliated by freezing new trade, recalling its students from Canada and cancelling flights between the two countries.
Hunt said he had spoken to immigration minister David Coleman about Qunun's case late on Tuesday. In a video clip of the meeting released by Thai immigration police, Alsheaiby is heard telling Thai officials: "From the moment she arrived, she opened a new account and her followers reached nearly 45,000 in a day. and I would have preferred it better if her phone was taken instead of her passport".
"He wanted to make sure that his daughter was safe. he told me that he wanted to take her home", he said, adding that her father denied Qunun's allegation that her family was abusing her physically and emotionally.
Under the hashtag #SaveRahaf, the young woman's desperate pleas became a social media sensation, and she was able to post live updates and videos from the Bangkok airport in both Arabic and English, racking up more than 80,000 followers.
"Indicating that if she had a valid claim we'd support their efforts to offer her settlement in Australia", Senator Wong told the ABC's AM on Thursday.
Saudi Arabia enforces male guardianship laws, which require that women, regardless of age, have the consent of a male relative - usually a father or husband - to travel, obtain a passport or marry.
Ms al-Qunun wrote of being in "real danger" if she was forced to return to her family.
"I am giving my family 48 hours (to) either stop or I will publish everything that will incriminate them", she threatened on Twitter. The 18-year-old captured the world's attention in a series of Twitter posts that at times read like an worldwide thriller - with very real consequences.
It praised Thailand for its actions in Alqunun's case, but said the country had not treated other asylum-seekers in the same responsible manner.
AFP was unable to contact Saudi authorities for comment on the footage.
"[Ms] Rahaf is not a political asylum case", he insisted.
In 2017, Dina Lasloom triggered an online firestorm when she was stopped en route to Australia where she planned to seek asylum.
The kingdom's human rights record has been under heavy scrutiny since the murder of journalist Jamal Khashoggi in the country's embassy in Istanbul a year ago.
Crown Prince Mohammed bin Salman had styled himself as a reformer, with women recently granted the right to drive, but these cases raise questions over how the regime exercises control.