The row burst into the open last Wednesday when the prime minister's sister Wei Ling and younger brother Hsien Yang released a statement accusing him of misusing his power and trying to milk their father's legacy for political gains.
Noting that the community has condemned the terrorists' ideology, PM Lee said the Government does not want other communities to cast doubts on this front.
The family dispute has affected Singapore's reputation and citizens' confidence in government, the PM declared on Monday. "As your Prime Minister, I apologise to you for this".
His father was Lee Kuan Yew the founder of Singapore and its prime minister for more than 30 years.
Mr. Lee Hsien Yang and Dr. Lee Wei Ling first publicly accused their brother of opposing Mr. Lee Kuan Yew's wish for the house to be demolished after his death in April past year.
The two siblings also claimed they feared the use of the organs of state against the both of them, as well as Mr. Lee Hsien Yang's wife Suet Fern.
This led to a series of exchanges that took place on Facebook and through public statements.
Last Saturday, Mr. Teo revealed that the ministerial committee looking into the future of 38 Oxley Road includes Cabinet members responsible for heritage, land issues and urban planning, namely Minister for Culture, Community and Youth Grace Fu, Minister for Law K Shanmugam, and Minister for National Development Lawrence Wong.
Added Minister-in-charge of Muslim Affairs Mr. Yaacob Ibrahim said in a Facebook post on Tuesday: "The two new cases of self-radicalisation (are) a grim reminder for our Muslim community that our young need urgent help and assistance".
He said he would address all questions on the matter when Parliament sits again on July 3. "I tried to deal with their unhappiness privately", he said. 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. "I had hoped that this would satisfy them", he said. "However, my siblings have made a decision to go out and make serious allegations, publicly", Lee said.
The Prime Minister of Singapore is Lee Hsien Loong.
"The Committee has tasked the relevant agencies to study a range of options for the property".
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?
As much as I would like to move on and end an unhappy experience for Singaporeans, these baseless accusations against the government can not be left unanswered.
Almost a week after his siblings publicly denounced him for engaging in dynasty politics, the PM has urged all members of parliament to "vigorously" question him and his cabinet colleagues about the matter at the next parliament sitting on July 3.
"As public servants, my ministers and I will always protect the integrity of our institutions, and uphold the strict standards separating private affairs from our public duties", said PM Lee.
"We are determined to fix the damage that has been done to Singapore", Lee pledged to the citizens.