The Attorney-General filed an application in the High Court for contempt of court proceedings against Li Shengwu, the 32 year-old Harvard educated grandson of the late Mr Lee, who ruled the country with an iron-fist from 1959 to 1990.

The action relates to a Facebook post Mr Li published on July 15 where he wrote that the "Singapore government is very litigious and has a pliant court system," and adding that because of previous legal action, foreign media had been cowed into self-censorship.

In the application the Attorney-General said the post was an "egregious and baseless attack" on the judiciary.

It asked that the post be deleted and that Mr Li sign and publish a written apology.

The government led by Mr Li's uncle Lee Hsien Loong had been trying for two weeks to get Mr Li to apologise, and even drafted an apology letter for him to sign.

The comments were only posted to Mr Li's Facebook "friends" but were later re-published by several websites.

In another Facebook post on Friday, Mr Li said it was not his intention to attack the Singapore judiciary or to undermine public confidence in the administration of justice.

"Any criticism I made is of the Singapore government's litigious nature, and its use of legal rules and action to stifle the free press," he wrote.

The family has been squabbling for more than a year over a house at 38 Oxley Road Singapore in which Lee Kuan Yew, who died a widower aged 91 in 2015, lived for most of his life.

Two of Mr Lee's three children have accused their elder brother, the prime minister Lee Hsien Loong, of abusing power to try to save the house as an historic monument, in defiance of their father's wishes.

The prime minister's motive was to bolster his own legitimacy and further the possibility of a Lee family dynasty, they said.

Claims of nepotism are highly sensitive in Singapore.

Mr Lee responded in a Facebook in June that he was "deeply saddened by the unfortunate allegations that they have made."

He said he and his wife Ho Ching deny "these allegations, especially the absurd claim that I have political ambitions for my son," referring to their second-eldest son Li Hongyi, a 30 year-old former army officer.

Mr Lee, who took over from his father's successor Goh Chok Tong in 2004, defended himself and his government against the accusations in parliament last month.

"In Singapore, everyone is equal before the law," he said.

"When the dust has settled on this unhappy episode, people must know that the government in Singapore operates transparently, impartially and properly."