Sitthichai Pokaiyaudom, the information minister, said he had called off immediate plans to file a criminal lawsuit against Google with the Thai courts on Friday.
However, he said authorities still wanted to charge the creators of the offending video clips.
|King Bhumibol Adulyadej is widely |
revered across Thailand [EPA]
"Thai police will ask for information from the company to file criminal charges against those who posted the clips," he said.
Earlier Sitthichai was quoted in the Bangkok Post saying he had received an official letter from the a Google vice president saying that the search giant did not want to promote hostile feelings over the videos.
According to the Post, Kent Walker pledged that the offending videos would be removed, although the process would take some time.
Walker said in the letter that the company slogan is, "Don't do evil", the Post reported.
A search of the YouTube site at 0500 GMT on Friday found several videos mocking the king and Thailand's response to the controversy still available.
The row erupted last month over a video posted on YouTube that mocked the Thai king, the world'd longest reigning monarch, regarded as semi-divine by many Thais.
Under Thai law, insulting the Thai king - known as "lese majeste" - is a criminal offence.
In response to the video Thailand's military-installed government announced it would block access to Youtube.
Although the original video has since been removed from the site, and the user who posted it barred from Youtube, the row has sparked several other users to post clips mocking Thailand and the Thai king.
Sitthichai said that if Google cooperates with Thai demands and removes the clips, "we will unblock the website immediately".
Commenting last month on the issue, he rejected suggestions that the government's response to the row was an attack on freedom of expression.
"People who create these [websites] are abusing their rights and clearly don't mean well for the country," he said.