The immensely popular 89-year-old had given his imprimatur to opposition leader Bill Shorten, who opinion polls suggest is the favorite to win the election. Shorten said on Friday that Hawke had given him his "blessing" when they last met at Hawke's home last week.
"Bob was generous in his last remarks to me, and he said we were doing really well and he was very proud of me," Shorten told Nine Network television. "I already feel a responsibility to millions of people to win. But sure, I want to do it for Bob as well. I don't want to let his memory down," Shorten added.
Many commentators believe Hawke's death at such a crucial time in the five-week campaign is a blow to the conservative Liberal Party-led coalition's chances of winning a third three-year term. Prime Minister Scott Morrison on Friday described Hawke as Labor's best prime minister.
"He was beyond politics. All Australians could connect with Bob Hawke," Morrison told Nine. "That I think was his great charm and his great strength and that enabled him to take the country with him on quite a number of important things."
Hawke was Australia's third longest-serving prime minister and the longest-serving Labor prime minister. He was ousted by his own party during a recession in 1991. But the economic reforms he made are often cited as a major reason that Australia has not had a recession since.
Morrison said on Friday the election result "is going to be incredibly close." An opinion poll published in The Sydney Morning Herald newspaper on Friday showed Labor ahead of the conservatives 51% to 49%.
But the difference is within market researcher Ipsos Australia's 2.3 percentage-point margin of error. The poll was based on a nationwide telephone survey of 1,842 voters this week from Sunday to Wednesday.
Shorten invoked the memory of another Labor hero on Thursday when he made his final campaign pitch in the same western Sydney venue where party leader Gough Whitlam gave what has been remembered as his "It's Time" speech in 1972.
"It's Time" was also the campaign slogan. Weeks after his speech, Labor won its first federal election victory since 1946 and Whitlam became a reforming prime minister. Morrison accused Labor of indulging in self-congratulation with the reminder of the Whitlam victory.
Whitlam, who died in 2014, is remembered for sweeping reforms including government-funded universal health care and free university education. But he is also remembered for financial mismanagement that led to his government being fired in 1975 by the Australian governor-general, who represents Australia's head of state, British Queen Elizabeth II.