Ms Gillard cut short her visit to Russia for the APEC summit after her father John died in Adelaide on Saturday.
Acting Prime Minister Wayne Swan offered his condolences from Brisbane.
"Anyone who saw Julia and her dad together recognised a very special, very close and very treasured father-daughter relationship and would be terribly saddened to hear of his passing," Mr Swan said.
"I know every member of the government is thinking of Julia, her mum and sister on hearing this sad news."
Mr Swan is expected to continue as acting prime minister when parliament resumes on Monday, while Ms Gillard grieves with her family.
Opposition Leader Tony Abbott also extended his sincere sympathies to the Gillard family.
"The thoughts of all Australians will be with the Prime Minister, Mrs Moira Gillard and their family at this difficult time," he said.
South Australian Premier Jay Weatherill said he was saddened by the news.
"Upon his daughter's elevation to the prime ministership, Australians came to know a gentleman who was kind, generous and proud of his daughter," Mr Weatherill said.
"He was obviously the inspiration behind her sense of justice for working people."
Governor-General Quentin Bryce, has sent Ms Gillard's family a private message.
Liberal MPs Andrew Laming, Andrew Southcott and Natasha Griggs expressed their condolences on Twitter.
Australian Greens leader Christine Milne said she was saddened to hear about the death.
"I was very saddened today to hear that the Prime Minister's father has died," she said in a statement.
"I extend to her my deepest sympathy and condolences and whatever support I can provide at this difficult time."
