Singapore's government has announced it is taking legal action against the grandson of founding leader Lee Kuan Yew over a Facebook post linked to an ongoing family feud.

In a statement late on Friday, 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 issue.

Li, an academic at Harvard University, is the eldest son of Lee Hsien Yang, the youngest child of the late Singapore leader.

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He had also posted links to a summary of the feud between his father, aunt and uncle.

The dispute among Lee Kuan Yew's three children - Lee Hsien Loong, the current prime minister; corporate executive Lee Hsien Yang; and neurologist Lee 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.

But Lee Hsien Loong's siblings say their brother is attempting to block the house's demolition to capitalise on their father's legacy for his political agenda.

The dispute spilled over onto social media with Li making the post.

'Egregious attack'

The attorney general's office described Li's post as "an egregious and baseless attack on the Singapore Judiciary and constitutes an offence of contempt of court".

It had asked Li to delete the post and sign an apology.

Instead, he clarified his comments in a post earlier on 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 Friday statement: "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."

Lee Hsien Loong has denied the allegations of blocking the building's demolition and ruled out suing his siblings.

Political opponents and dissidents have previously been hit with financially ruinous defamation lawsuits filed by Singapore's leaders.

Played out across social media, details of the feud have kept entertained a country unused to open criticism of its political leaders.