Furious top brass in the South East Asian nation reportedly want the clip taken offline and the Bangkok Post is reporting the entire country could lose its access to Facebook as early as Tuesday morning (local time) if this isn't removed.
The Thai Government has backed down on a threat to close Facebook in the kingdom if the company failed to remove pages considered offensive to the monarchy.
As of the end of the workday on Monday, Facebook scrubbed more posts, leaving under 100 still live in Thailand.
Facebook, which opened an office in Thailand in 2015, is the biggest social network in the country.
In a statement on Tuesday, Facebook did not say whether it would now take action as a result of the fine.
However, there would be no immediate measures to block Facebook, Takorn Tantasith, secretary-general of Thailand's telecoms commission, told reporters, adding that bureaucracy had held up the process of removing the 131 impugned content items.
Much of that is deemed in violation of the country's lese majeste law, the harshest in the world.
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"If, after careful legal review, we find that the content is illegal under local law we restrict it as appropriate and report the restriction in our Government Request Report", Facebook has said previously.
Article 112 of Thailand's criminal states that: "Whoever, defames, insults or threatens the King, the Queen, the Heir-apparent or the Regent, shall be punished with imprisonment of three to 15 years".
Addressing speculation the government was building a case to pull the trigger on blocking Facebook in the kingdom, Takorn said his agency made no such proposal, as it has been cooperating with the authorities.
The trouble with having the ISPs do the blocking is that it is very hard for them to do so selectively or by posts or URLs because the communication between a user's browser and the Facebook website is encrypted. Facebook was still accessible in Thailand on Tuesday after the deadline.
Internet service providers are able to block access to most pages, but said some 600 could not be shut down because of encryption.
Watchdog CNIL said its fine - which was imposed on both Facebook Inc and Facebook Ireland - was part of a wider European investigation also being carried out in Belgium, the Netherlands, Spain and Germany into some of Facebook's practices.
The Thai government said there are 131 files on Facebook that are a threat to national security.