Talk of bushfires and volunteer firefighters dominate meeting between Prince William and Prime Minister Tony Abbott.

Prime Minister Tony Abbott has made no secret of his love of the royal family and he was more than happy to welcome another prince to Sydney.

Mr Abbott, who recently and controversially reintroduced knighthoods and damehoods to Australia, met Prince William – second-in-line to the throne – at Admiralty House on Wednesday.

The Duke and Duchess of Cambridge are making their first official visit as a couple to Australia. William has visited three times before, including once with his parents Charles and Diana when he was the same age as George.

Kate and Prince George did not attend Wednesday afternoon’s meeting in the elegant drawing room of Admiralty House, the harbourside official residence of the governor-general.

Prince William, Mr Abbott and their companions enjoyed a cup of tea during the meeting in the richly appointed room with views onto rolling gardens, the sunny harbour and glimpses of the Opera House.

Mr Abbott was focused on talking about Australia’s volunteer firefighters after the duke and duchess visited the Blue Mountains to meet those affected by the bushfires six months ago.

He told the duke about the great spirit of the Rural Fire Service and mentioned his own work with the volunteer brigade in a meeting at Admiralty House in Sydney.

Mr Abbott, a member of the Davidson RFS branch, told the prince: “I’m a member of the local volunteer Rural Fire Service,” before discussing the ferocity of the fires that burned for a fortnight and the spirit of volunteer firefighters.

“These guys will respond to the needs even if they’ve got to neglect their own properties. It’s a great embodiment of the volunteer spirit, a great example of mates looking after mates.”

Mr Abbott asked William, who changed into a navy suit and red printed tie for the meeting, if he had enjoyed his visit to the Blue Mountains.

“A very good day, thank you. There were some incredible stories,” the prince said.

William remarked to Mr Abbott how stoic the survivors who’d told him their stories had been.

He recounted being told by one resident of his efforts to defend his own house before helping save his neighbour’s property.

Mr Abbott also told the prince that locals were worried that tourists and visitors thought the Blue Mountains was still devastated by fire.

“But it’s amazing how quickly the bush recovers and there’s still businesses, attractions,” Mr Abbott said.

The prince mentioned his visit to the Three Sisters.

“It was a beautiful area,” he said.

Mr Abbott, who will host the royal couple at a lunch at Parliament House in Canberra next Thursday, hinted that he might appear at other events while the royals are in Sydney.

“Great to meet with the Duke of Cambridge today – Looking forward to other events with the visiting Royals over Easter,” he tweeted after the meeting.

The royal couple will be at the Royal Easter Show and later Manly Beach in Mr Abbott’s electorate on Friday. Mr Abbott is also a member of the Queenscliff Surf Lifesaving Club.

On Sunday, they’ll be at Taronga Zoo – near Admiralty House.

It’s not the first time Mr Abbott has welcomed a member of the royal family. Last October, he told William’s younger brother Harry – who was visiting during Fleet Week: “Prince Harry, I regret to say not every Australian is a monarchist. But today everyone feels like a monarchist.”