Lee Hsien Yang and his sister, Wei Ling, released a strongly worded six-page statement Wednesday accusing their brother of abusing his powers and saying they they had lost confidence in his leadership.
"The country must be bigger than one family," Hsien Yang told AFP in an email.
The quarrel exposed the issue of succession when the estranged siblings claimed that Lee and his influential wife, Ho Ching, harboured political ambitions for their son, Li Hongyi.
Lee Hsien Yang, who went into the business world rather than government, said his own son -- a Harvard academic -- had no interest in entering government.
"He believes it would be bad for Singapore if any third generation Lee went into politics," he said. "My elder son and my views on politics are entirely aligned."
Prime Minister Lee had denied the allegations and expressed sadness that the feud has erupted into public view.
He described the claim about his son as "absurd" and Li Hongyi said in a Facebook post Thursday: "For what it is worth, I really have no interest in politics."
Singapore has been ruled continuously by only one party -- the People's Action Party -- since 1959 when the island gained self-rule from Britain.
Since independence in 1965, the city-state has known only three prime ministers, two of them from the Lee family. Relative prosperity -- as well as legal restraints on dissent -- has helped to insulate the leadership, but observers say the spat comes as a sensitive time for the country as it faces uncertainty over the future of its economy and governance.
Honouring a legacy
The siblings' grievances centre on the future of their family home.
Lee Kuan Yew wanted the house demolished to avoid it becoming a monument, a decision Hsien Yang and and Wei Ling supported. The siblings accuse the prime minister of defying their father's instructions.
News of the spat rippled across social media in a nation unaccustomed to picking through salacious morsels of the private lives of its leaders.
"I wish more of us will dare to speak up for what we feel is wrong... Even if it is against the most powerful man in the country, or even if it is against our own siblings and family members," one commentor, Ali Fadli Mohd, posted on Hsien Yang's Facebook page.
"It takes courage when they are both."
Others were more sanguine, criticising the siblings for going public with a family matter, or dismissing the subject of the feud as a tiff between elites.
The news was also on the front page of the main English daily the Straits Times, which led on the prime minister denying the allegations.
Singapore's tough laws against protests and curbs on press freedom have stifled political discussion and defamation suits have been levelled at opposition figures.
Asked if he expected a legal challenge from his brother, Hsien Yang said: "You have to ask Lee Hsien Loong. Truth is the simplest defence for defamation actions."
Patriarch Lee, who died in March 2015 aged 91, served as the country's first prime minister and transformed Singapore from a relatively poor British colonial outpost into one of the world's most affluent societies.
Lee Hsien Loong, 65, who became prime minister in 2004 said the allegations hurt the legacy of their father.
But asked if the public quarrel would tarnish their father's legacy and Singapore's global standing, Hsien Yang said: "I am seeking to honour my father's values, which is a key part of his legacy."
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)