(CNN) Singapore's Prime Minister has made a rare public apology for a family spat that has gripped a city unused to elites airing their grievances.

Lee Hsien Loong refuted allegations that he has violated the will of his late father, Singapore's former leader Lee Kuan Yew, for his own political gain.

"I deeply regret that this dispute has affected Singapore's reputation and Singaporean's confidence in the government. As your Prime Minister, I apologize to you for this," Lee said in a video statement posted to Facebook that also aired on national TV.

The high esteem in which most Singaporeans hold their former leader and the city-state's strict censorship laws have made the public spat something of a political soap opera for the Singapore's 5.5 million people. The extent of any political fallout is still unclear.

The Lee family is fighting over the future of their late father's home in central Singapore. The Prime Minister wants to preserve the house, while his brother and sister want to demolish it.

"As the eldest of the siblings, it grieves me to think of the anguish it would have caused our parents if they were alive," he said.

Lee went on to say he's done all he can to avoid the current situation.

He said he would also refute the allegations in Parliament on July 3, adding that he has instructed the ruling People's Action Party whip to be lifted -- allowing members of parliament to ask questions and not be bound by the party position.

"I hope that this full public airing in Parliament will dispel any doubts that have been planted and strengthen confidence in our institutions and our system of government," Lee said.

The house at the center of the squabble

The family patriarch, Lee Kuan Yew, is credited with turning Singapore from a colonial trading post into a thriving city-state. He served as the country's leader from 1959 to 1990 and died in 2015.

In his will, Lee had asked for his home -- a pre-war bungalow the country's founding father lived in since the 1940s -- to be demolished immediately after his death, or if his daughter, Lee Wei Ling, preferred to live in it, after she moved out.

All three of the elder Lee's children publicly issued a statement in 2015, saying they hoped the state would honor their father's wishes. Lee Hsien Loong also said he would recuse himself from all government decisions involving the home.

However, in a statement released last week, Lee's sister and brother -- Lee Wei Ling and Lee Hsien Yang -- claimed the Prime Minister and his wife are behind what is represented as government initiatives to preserve the house.

They further alleged Lee threatened them and demanded their silence over their father's wishes "hoping to inherit the faith Singaporeans had in Lee Kuan Yew through the visible symbol of the house."

The Prime Minister forcefully denied that charge in his statement.

"These allegations go beyond private and personal matters and extend to the conduct of my office and the integrity of the government. As much as I would like to move on and end an unhappy experience for Singaporeans, these baseless accusations against the government cannot be left unanswered. They must be and will be dealt with openly and refuted," he said.

The outside the house of Singapore's late founding father Lee Kuan Yew at Oxley Rise in Singapore on April 11, 2016.

Lee said his father left the house to him.

"My siblings were not happy about this. I tried to deal with the unhappiness privately," Lee said, including offering to sell the house to his sister for $1. Lee said that offer failed, so then he sold the house to his brother at a "fair market value" and donated the proceeds to charity.

"There should be no reason for any quarrel, since I no longer own the house and I do not take part in any government decisions on the house. However, my siblings have decided to go out and make serious allegations, publicly," Lee said.

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On Tuesday, Lee Hsien Yang responded to the Prime Minister's public message with yet another post on Facebook, suggesting the issue is not going away any time soon.

"We object to LHL's flip-flopping about Lee Kuan Yew's demolition wish," he said.

"We asked a simple question, that he has refused to answer for a week: Was our father, Lee Kuan Yew, unwavering in his demolition wish? Yes or no?"

While the elder Lee was lauded for his economic accomplishments, he also was responsible for stringent laws and regulations that dictated most, if not all, aspects of society -- including media and political freedoms, censorship and even the selling of chewing gum.