After three weeks of accusations and rebuttals, the three children of founding prime minister Lee Kuan Yew have taken a step towards resolving an acrimonious public feud that started over the fate of their family home.

Dr Lee Wei Ling and Mr Lee Hsien Yang, younger siblings of Prime Minister Lee Hsien Loong, said yesterday that they welcome their elder brother's desire to settle their quarrel in private, and "look forward to talking without the involvement of lawyers or government agencies".

For now, they will stop posting further allegations and evidence against him on social media, they added, but with one condition: Provided that their wish and their father's desire to demolish the house at 38, Oxley Road "are not attacked or misrepresented".

This means not "attacking" their father's last will and taking it as his last word on the house, they said.

In a seven-page statement on Facebook, they said: "(We) do not wish to see Singapore embroiled in a never-ending public argument... Ultimately, it is up to the Government, and the people of Singapore, to decide whether and how to hold Lee Hsien Loong to account."

Despite this, they also released a 10-page summary of the allegations they have made against PM Lee and the evidence they have cited to prove their case.

They warned that there is evidence they "have yet to show", some of which is "too complex" to be presented online. They are keeping the option open to show it "to a truly open and independent investigation, if there ever is one", they added.

The two had gone public with their dispute on June 14, accusing PM Lee of abusing his power and thwarting the demolition of their father's house at 38, Oxley Road for political gain.

PM Lee, refuting these charges in a two-day Parliament sitting this week, said the Government had merely been ensuring that due process was followed, and he had kept his private and public interests separate by recusing himself from all government decisions on the house.

He also said he hoped to reconcile with his siblings one day.

In their latest statement, the younger siblings said they have not spoken to their elder brother since April 12, 2015, when their father's will was read. Describing that day as the point of no return, they said PM Lee had shouted at and intimidated them when they quarrelled over their father's wish.

The sticking point was the interpretation of the late Mr Lee's wish for the house as expressed in a clause in his last will. He died on March 23, 2015, aged 91.

The younger siblings believed their father was uncompromising in wanting the house pulled down as he did not want Singaporeans to create a cult around him, while PM Lee believed he was open to preserving parts of it because of its historical value.

The basement dining room of the house was where the People's Action Party was founded by the late Mr Lee and his friends.

The two younger siblings said yesterday that they were "gobsmacked" when PM Lee told them he had hired a lawyer to deal with the matter.

"Soon, Hsien Loong ceased to communicate with us directly," they said. "The first Chinese New Year reunion after our father's death, our brother invited all relatives except us."

They also said that they had tried to reach out to PM Lee through intermediaries over the past two years, without success.

On why they went public, Dr Lee and Mr Lee Hsien Yang said: "Would you keep quiet, if you were executors of your father's will, and your brother abused his position to challenge your father's court- proven will and undermine your father's dying wish?"

They added that while their father had made "backup plans" in his will in case his wish was not fulfilled, it did not mean he "desires or accepts that the event should happen".

PM Lee had raised serious misgivings about the will, saying it was not clear who drafted it, but his siblings did not address this in their statement yesterday. They said: "We hope that he will cease attacking the will. If the Government respects the separation of powers, it should treat Lee Kuan Yew's will as the last word on the matter."

A ministerial committee formed to study options for the late Mr Lee's house had raised their ire after asking them questions on the late Mr Lee's will.

Yesterday, Dr Lee and Mr Lee Hsien Yang said they were glad that the committee has acknowledged it has no authority to rule on the validity of the will, and would not be doing so.

But they added that they would not be making "further submissions to the committee in its current form".

Apologising to Singaporeans for taking their quarrel online, the siblings said they did so because they had no "unfiltered access" to mainstream media.

"We have made a lot of mistakes along the way; please forgive us," they said.

They acknowledged the support they have received, and said they also recognised that some people had different views on the house and its preservation.

"We respect your views and your voice. You have our heartfelt thanks," they said.