Rahaf Mohammed al-Qunun told AFP she ran away from her family while travelling in Kuwait because they subjected her to physical and psychological abuse.
The 18-year-old said she had planned to seek asylum in Australia and feared she would be killed if repatriated by Thai immigration officials who stopped her during transit on Sunday.
The incident comes as Saudi Arabia faces intense scrutiny over the shocking murder of journalist Jamal Khashoggi last year, which has renewed criticism of the kingdom's rights record.
Thai immigration chief Surachate Hakparn had said Sunday that Qunun was denied entry because of her lack of documents.
But he made an abrupt about-face the next day, following a global media frenzy as the young woman pleaded on Twitter for different countries to help her.
"If she does not want to leave, we will not force her," he told reporters at Suvarnabhumi airport on Monday, saying the UN refugee agency (UNHCR) would be able to meet her.
"The UNHCR and I will... listen to what she wants, whether or not she wants to receive asylum to which country, and we will help coordinate."
Qunun was stopped by immigration because Saudi Arabian officials contacted them to say she had fled her family, he added.
If she wished to stay in Thailand, the UN would have to verify the legitimacy of her asylum claims, Surachate said.
"Thailand is a land of smiles. We will not send anyone to die," he added. "We will take care of her as best as we can."
- Barricaded in -
The UNHCR said it had been granted access to Qunun at the airport "to assess her need for international refugee protection and find an immediate solution for her situation".
Qunun had posted a video on Twitter of her barricading her hotel room door with furniture.
She said Saudi and Kuwaiti officials had taken her travel document from her when she landed -- a claim backed by Phil Robertson, deputy Asia director at Human Rights Watch.
But at the press conference, Surachate said it was Thailand's "procedure to take the passport of anyone who we deny entry to."
Earlier a Thai court dismissed an injunction to block Qunun's deportation, said human rights lawyer Nadthasiri Bergman, who filed the request.
"They said we do not have enough evidence," she told AFP, adding she planned to appeal.
Abdulilah al-Shouaibi, charge d'affaires at the Saudi embassy in Bangkok, told Saudi-owned TV channel Khalijia that the woman's father had contacted the diplomatic mission for "help" bringing her back.
But he denied that her passport had been seized and that embassy officials were present inside the airport.
A Twitter statement from the Saudi embassy in Bangkok said Qunun was stopped by Thai authorities for "violating the law".
"She will be deported to the State of Kuwait where her family" lives, it added. Qunun, however, told AFP that she was only travelling in the Gulf state.
- 'Facing grave harm' -
The ultra-conservative Saudi kingdom has long been criticised for imposing some of the world's toughest restrictions on women.
That includes a guardianship system that allows men to exercise arbitrary authority to make decisions on behalf of their female relatives.
In addition to facing punishment for "moral" crimes, women can also become the target of "honour killings" at the hands of their families, activists say.
If sent back, Qunun told AFP she would likely be imprisoned and was "sure 100 percent" her family would kill her.
"My family is strict and locked me in a room for six months just for cutting my hair," she said.
HRW's Robertson said she "faces grave harm if she is forced back to Saudi Arabia", and that Thailand should allow her to see UN officials and apply for asylum.
"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 said.
"She has clearly stated that she has renounced Islam which also puts her at serious risk of prosecution by the Saudi Arabian government."
An Australian government spokesman said the claims made by Qunun "that she may be harmed if returned to Saudi Arabia are deeply concerning" and they are monitoring Qunun's case "closely".
Australian embassy representatives in Bangkok have reached out to Thai authorities and the UNHCR to "seek assurances" that she will be able to access the "refugee status determination process".
The UNHCR said that according to the principle of non-refoulement, asylum seekers cannot be returned to their country of origin if their life is under threat.