Singapore’s government is to take legal action against the grandson of founding leader Lee Kuan Yew over a Facebook post linked to a family feud that has gripped the city state.

The spat between Lee’s three children – the current prime minister, Lee Hsien Loong, the corporate executive Lee Hsien Yang, and Lee Wei Ling, a neurologist – centres on what to do with their late father’s home, a century-old bungalow.

Lee, who is widely credited with transforming Singapore from a British colony to one of Asia’s wealthiest countries, stated in his will that he wanted the house torn down to avoid the building of a personality cult around him.

But the prime minister’s siblings said their brother is attempting to block the house’s demolition to capitalise on their father’s legacy for his own political agenda.

In a statement late on Friday, the attorney general’s chambers (AGC) said it was applying for permission to prosecute Lee’s grandson Li Shengwu over a Facebook post last month in which he alleged that the government was litigious and was stifling freedom of speech over the spat.

Li, an academic at Harvard University, is the eldest son of Lee Hsien Yang. 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”. It had asked Li to delete the post and sign an apology.

Instead, he clarified his comments in a post 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.”

The 65-year-old prime minister has denied the allegations of blocking the building’s demolition but said he would not sue 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 enthralled a city state unused to open criticism of its political leaders.