The spat between Lee Kuan Yew's three children -- current prime minister Hsien Loong, corporate executive Hsien Yang, and neurologist Wei Ling -- centres on what to do with their late father's home, a century-old bungalow.
Lee Kuan Yew, who is widely credited with transforming Singapore from a British colony to one of Asia's wealthiest countries, stated in his will that he wants the house torn down to avoid the building of a personality cult around him.
In a statement today, the Attorney-General's Chambers (AGC) said it was applying for permission to prosecute Li Shengwu over a July Facebook post in which he alleged the government was litigious and stifling freedom of speech over the spat.
Li, an academic at Harvard University, is the eldest son of Hsien Yang.
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He had also posted links to a summary of the feud between his father, aunt and uncle.
The AGC had described his post as "an egregious and baseless attack on the Singapore Judiciary and constitutes an offence of contempt of court".
Instead he clarified his comments in a post earlier Friday, saying that it was not his intention to attack the judiciary.
"Any criticism I made is of the Singapore government's litigious nature, and its use of legal rules and actions to stifle the free press," he said.
The AGC said in its statement today: "As Mr Li has failed to purge the contempt and to apologise by the extended deadline, an application for leave to commence committal proceedings for contempt against him will today be filed in the High Court."