Muralitharan withdrew from the two-match series for personal reasons, giving 34-year-old Warne an opportunity to pass his mark of 527 Test wickets.
"I'm sure he'll (Warne) be given a chance. It would be a shame if it gets to the stage where he doesn't hold the record at all because I think he really deserves to have at least held it for a certain amount of time," said Ponting, who missed Australia's 149-run victory in the first Test because of a family death.
"So we'll hope that he gets a good bowl up in Cairns and he can take eight more wickets."
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Paceman Glenn McGrath's seven wickets after a 12-month injury layoff took his tally to 437 and moved him into fourth on the list.
"(McGrath) was sensational. If he's bowling that well and Warney's bowling as well as he has done of late, then it certainly adds a lot of aura to our team," said Ponting, who captained Australia to last year's World Cup triumph.
Matthew Elliott, who batted at number three in Ponting's place and made 1 and 0, is likely to make way for the skipper for the second Test which starts on Friday.