Abbott congratulated the Danish prince on his long list of achievements: mastery of three foreign languages, military service and - closer to Mr Abbott's ever-competitive heart - running a marathon in an impressive three hours and 22 minutes.
"Many of us in this building would wish to emulate that feat," said Mr Abbott, whose own personal best is a comparatively feeble three hours and 47 minutes.
But Mr Abbott was selling Frederik short. "My personal record in a marathon is three hours and six minutes," Frederik corrected him to the amusement of hundreds of assembled guests. Frederik paused.
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"But it's not about winning ... It's about succeeding," he added. "And this is what I've done six times."
Frederik and Mary, who was wearing a black and white knee-length floral dress with her hair tied back into a simple but elegant bun, arrived in Canberra on Tuesday on the second leg of a week-long official Australian visit.
Their first engagement was a meeting with Prime Minister Julia Gillard, who told the reception the couple's romance was a modern-day fairytale.
"A beautiful young woman meets a handsome prince and they live happily ever after," Ms Gillard said. Local indigenous leader Janette Phillips said Princess Mary had given Australian women everywhere fresh hope that "Prince Charming" really was out there.
But it wasn't all jokes and gooey sentiments. Ms Gillard seized the opportunity to highlight the successes of Denmark's own carbon pricing scheme, imposed almost two decades ago.
"I know that as Australia undertakes its journey towards a low carbon future, we have a great partner in Denmark." Frederik was keen to take up the environmental theme.
"Climate change, scarcity of resources and a world population that continues to grow make it unsustainable to continue business as usual," he said. "We need change, we need innovation."
To help achieve that, he urged closer ties between Australian and Danish companies and a heavy emphasis on research and development in the alternative energy market.
The royal couple later met Mr Abbott in his office before attending a seminar on green growth and touring the National Gallery of Australia, the National Portrait Gallery and the National Arboretum.
They were scheduled to finish the Canberra leg of their trip by laying a wreath at the Australian War Memorial.
Frederik and Mary will spend the next few days in Melbourne.
