Mr Lee Hsien Yang and Dr Lee Wei Ling, the siblings of Prime Minister Lee Hsien Loong, said they have never asked the Government to let them demolish their late father's house immediately.
Instead, they want to be able to do it only after Dr Lee moves out of the house, Mr Lee Hsien Yang said in a Facebook post.
A series of Facebook exchanges erupted yesterday between him and Dr Lee on the one side, and Senior Minister of State for Finance and Law Indranee Rajah on the other, in the ongoing dispute over the house of the late Mr Lee Kuan Yew.
Their exchange revolves around two questions. These are:
•Why must the Government commit to a decision on whether to demolish the 38, Oxley Road house now?
•Why is a ministerial committee tasked to consider options for the house unable to make a binding decision on what to do with it?
In his post, Mr Lee Hsien Yang said that neither he nor his sister - executors of the late Mr Lee's will - asked the Government to allow them to demolish the house right away.
This drew a response from Ms Indranee, who said he had not answered the "basic question" of why the Government was being asked to make a decision now on whether to demolish the house, when the decision might not need to be taken for 20 to 30 years.
This is because Dr Lee is still living there, and a decision would have to be made only when she moves out.
"Why is the Government being asked to decide now? What is the urgency? This question has not been answered," she wrote.
She also said: "As Mr Lee Hsien Yang would know, this Government cannot, as a matter of principle, bind a future government that is elected by the people 20 to 30 years from now."
Addressing Ms Indranee's question on why a decision had to be made now, Dr Lee wrote yesterday afternoon that "the answer is simple, we seek to honour our father's final request in his will".
Both Dr Lee and Mr Lee Hsien Yang also took aim at the ministerial committee tasked to consider options for the house at 38, Oxley Road.
Pointing to a June 17 statement by Deputy Prime Minister Teo Chee Hean about the committee, Dr Lee said: "A few days ago, DPM Teo revealed that the committee could make no commitment, only a non-binding recommendation."
Given that the committee was never meant to make a binding decision on the house, she added, the committee cannot be said to have been set up for the purpose of considering the demolition request.
DPM Teo had said one reason for setting up the committee was that soon after Mr Lee died in 2015, Dr Lee and Mr Lee Hsien Yang wanted the Government to commit immediately to demolishing the house. DPM Teo also said some Cabinet ministers wanted to give a future government "a set of options that came from ministers who had personally discussed this matter with Mr Lee Kuan Yew".
Mr Lee Hsien Yang, however, said yesterday that the committee was focused primarily on "parroting PM Lee's attacks on our father's will".
He also said that before the committee was formed, an offer by him and Dr Lee - to build a memorial garden on the Oxley Road site after demolishing the house - was rejected by PM Lee.
"SMS Indranee is pretending that the secret committee had an open discussion with Lee Kuan Yew's estate about options for the house," he said.
"Nothing could be further from the truth. The committee refused to state either the options it was considering or its final deliverable."