While Payne said there was "no timeframe" for a decision, Thailand's immigration department chief, Surachate Hakparn, said it should become clear by Friday evening where Qunun would be granted asylum. No other details were immediately offered.
Saudi teen Rahaf Mohammed al-Qunun is now staying in a Bangkok hotel under the care of the United Nation's refugee agency (UNHCR), which has been processing her application for refugee status ahead of possible resettlement in Australia.
Alqunun was on her way to Australia last Saturday but was stopped at a Bangkok airport by immigration police who seized her passport.
She then barricaded herself inside a hotel room, posting live updates on social media in which she said she feared for her life should she be forcibly returned to her family.
On Wednesday, Thai officials had allowed her to assume temporary protection of United Nations officials.
Qunun alleges abuse by her family - who deny the allegations - and rights groups also said she had renounced Islam, risking prosecution in conservative Saudi Arabia.
Several women had been forced to return home in recent years, they say, adding that many similar cases had gone unreported.
However, Ms Qunun sent a series of tweets pleading for help from her airport hotel room, and her case was picked up by Human Rights Watch and journalists.
Canada's acceptance of Alqunun is likely to further upset its relations with the Saudi rulers.
Canadian Prime Minister Justin Trudeau confirmed that his country had granted her asylum.
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It was unclear why Qunun chose to seek asylum in Canada after initially expressing a desire to live Down Under.
It all began with a simple tweet last summer, after Amnesty International learned the Saudi government had arrested several female human rights activists.
Australian Minister for Foreign Affairs Marise Payne talks to members of the press during a press conference at the Australian Embassy in Bangkok, Thailand, 10 January 2019.
Around mid-day on Friday, her Twitter account, @rahaf84427714, went offline after she posted that she had "bad and good news!" Australia's Education Minister Dan Tehan said Saturday that Australia had moved quickly to process her case but Canada made a decision to take her in. She later told reporters that Australia was assessing Al-Qunun's request for resettlement.
"The safety of Ms Al-Qunun has always been the Australian Government's primary concern, and we have been working with the UNHCR and global partners to ensure her claim is assessed appropriately", he said.
"She's just been receiving a lot of death threats", McNeill said on Twitter. The Saudis also sold Canadian investments and ordered their citizens studying in Canada to leave.
The ultra-conservative Saudi Arabia has come under fire since the murder of journalist Jamal Khashoggi in the country's consulate in Istanbul a year ago. Al-Araibi, however, faces a court trial in Thailand for extradition as requested by Bahrain for his role in anti-government protests.
A Saudi woman has been given refugee status by the United Nations and is being considered for resettlement by the Australian government.
"Canada has been unequivocal that we will always stand up for human rights and women's rights around the world", he said.