Ponting said there were concerns about middle-order's ability to play spin but the return of Warner and Smith has strengthened the team.
Melbourne: Former skipper Ricky Ponting believes defending champion Australia's ability to bowl and play spin will define their success in the upcoming World Cup beginning May 30.
"The thing that will define Australia's success in the World Cup is, one, how well they bowl spin and, two, how well they play it," Ponting was quoted as saying by the 'Sydney Morning Herald'.
"That's been their Achilles' heel the last 12 or 18 months. With [Adam] Zampa bowling well now, Nathan Lyon's obviously in the squad and Glenn Maxwell's done a good job with the ball whenever he's played."
Ponting said there were concerns about the middle-order's ability to play spin a year ago but the return of David Warner and Steve Smith has strengthened the team.
"And I think some of our middle order are probably slightly better players of spin now than they were 12 or 18 months ago," said the 44-year-old, who won Australia the 1999 World Cup as a player, before guiding the team to successive titles in the next two editions as a captain.
"With Warner there now and Steve Smith coming back in, the middle order looks a lot better against spin bowling than it probably was."
Warner and Smith had served a 12-month ban for their respective roles in the ball-tampering scandal that rocked Australian cricket in March last year.
They returned to competitive cricket at the Indian Premier League with Warner amassing 692 runs in 12 matches and Smith scoring 319 runs in 12 matches and leading Rajasthan Royals to three wins in five matches.
"They're both playing really well. Steve Smith still thinks he's not probably 100 per cent fit just yet - but he's not far away. And Warner's been the dominant batsman in the IPL," Ponting said.
There are concerns that Smith and Warner will be targeted by the crowd during the World Cup with English cricketer Moeen Ali urging the spectators to treat them with respect.
"Those two coming in, obviously they're class players - they'll have their fair share of issues to deal with from the crowds and stuff when they get over there," he said.
"But they're big boys. They've been there and seen it all before. I'm sure they'll be fine."
Australia will begin their campaign against Afghanistan on June 1 at Bristol.