Australian Foreign Minister Julie Bishop visited the Singapore High Commission in Canberra on Thursday to sign the condolence book for the late Mr Lee Kuan Yew.
In her message, Ms Bishop wrote: "Our thoughts are with the people of Singapore as they mourn the loss of their founding father - a giant of his times," according to Singapore's Ministry of Foreign Affairs.
Australian Prime Minster Tony Abbott will attend the funeral of Mr Lee on Sunday, according to media reports.
Both the governments of Australia and New Zealand passed parliamentary motions to mourn the passing of Mr Lee, as a testament to the high regard for Singapore's founding prime minister's achievements and his contributions to promote bilateral relations with key partners.
In his condolence motion speech in the Australian Parliament on Tuesday, Mr Abbott noted Mr Lee's warning to Australia more than 30 years ago. During a visit in 1980, Mr Lee warned that Australia needed to open its economy and try to reduce inflation and unemployment, or risk becoming the "poor white trash of Asia".
In his motion speech, Mr Abbott praised Mr Lee for "spur(ring) this country at a critical time in our history to be better than we might have been".
Praising Mr Lee for helping to achieve "one of the most remarkable economic success stories in history", Mr Abbott said the "great nation-builder" had been a trailblazer for other countries such as South Korea and China.
"Lee Kuan Yew did not just lead his country; he made his country," he added.
"Singapore and Australia are natural partners, and I hope that over time, our relationship with Singapore will be as easy, as close and as familial as it has long been with New Zealand. And, if so, that too will be part of Lee Kuan Yew's legacy."