The Attorney-General's Chambers (AGC) said it decided to act after Li Shengwu, 32, the eldest son of Lee Hsien Yang, and nephew of the Prime Minister failed to remove the Facebook post and to apologise by an extended deadline of 5pm yesterday.
In the Facebook post on July 15, which Li set to "friends only" privacy setting, but which was published by several websites and widely circulated on social media, he said foreign media had been cowed into self-censorship because of previous legal action.
The article was titled Singapore, "A Model Of Orderly Rule, Is Jolted By A Bitter Family Feud".
He also included a link to a 2010 New York Times commentary that was critical of the late Lee Kuan Yew and the government over what it deemed as censorship of the foreign press.
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In that letter, Senior State Counsel Francis Ng noted that the New York Times article described the Singapore government as "an authoritarian regime which aggressively uses the Singapore judicial system to silence its critics, even where such criticisms are fair or valid".
The article also described the late Lee Kuan Yew as the designer of "draconian press laws", which have been used to suppress legitimate criticism, he wrote.
Referring to Li's Facebook post, Ng said: "The clear meaning of the post, in referring to 'a pliant court system', is that the Singapore judiciary acts on the direction of the Singapore government, is not independent, and has ruled and will continue to rule in favour of the Singapore Government in any proceedings, regardless of the merits of the case".
The AGC said it had given Li until 5pm on July 28 to delete the post.
Li then wrote to the AGC to request an extension of time till 5pm on August 4 to respond to the AGC's letter.
But he failed to purge the contempt and to apologise by the extended deadline, the AGC said.
In a Facebook post earlier yesterday, Li said the post was not an attack on the judiciary.