The statement follows a month of accusations exchanged between the two siblings, Lee Hsien Yang and Lee Wei Ling, and their older brother who is currently the prime minister, The Straits Times and Asia News Network reported.
"We do not wish to see Singapore embroiled in a never-ending public argument. For now, we will cease presenting further evidence on social media, provided that we and our father's wish are not attacked or misrepresented," the two siblings said in a seven-page statement on Facebook.
The two Lees and Prime Minister Lee Hsien Loong had been at odds over their father's intention for his house at 38 Oxley Road.
Lee Hsien Yang and Lee Wei Ling have claimed Singapore's founding prime minister requested the house be demolished as it states in his will.
But their older brother and parliamentarians in Singapore are questioning the status of the will, including the author of the draft document, according to Singapore's TODAY online.
"The allegations are very bare. But I still want to know who drafted the last will. There are still questions as to whether it contradicts [Lee Kuan Yew's] intentions," said parliamentarian Lim Biow Chuan.
The dispute became public when the two siblings accused Lee Hsien Loong of obstructing demolition in order to "inherit" their father's political capital, according to reports.
Lee has said his father had expressed a wish the house remain preserved for its heritage value and historical significance.
The basement dining room was the meeting site for founding members of the People's Action Party, Singapore's ruling party since 1959.
Lee Kuan Yew died in 2015 at the age of 91.