Richie Benaud has been described as an Australian treasure and a cricket icon after his death, aged 84.

The former Australian captain and commentary doyen died overnight in his sleep after battling skin cancer.

“Our country has lost a national treasure,” Cricket Australia chairman Wally Edwards said in a statement on Friday.

“After Don Bradman, there has been no Australian player more famous or more influential than Richie Benaud.”

Prime Minister Tony Abbott said there would barely be an Australian in the past four decades who hadn’t listened to Benaud’s commentary.

“He was a very effective cricketer, a great captain, a great character and great personality,” Mr Abbott told ABC Radio.

“He has been a part of the lives of millions of Australians and he will certainly be very much missed.”

In Benaud’s native Sydney, NSW Premier Mike Baird ordered flags be flown at half-mast on Friday in honour of Benaud and offered a state funeral.

Benaud was described as the “Godfather of Australian cricket” by former International Cricket Council, and Cricket Australia, chief executive Malcolm Speed.

Australia’s current Test captain Michael Clarke said he was a “great player and a great captain, a wonderful leader of men”.

“He loved winning. He helped the Australian team have the attitude where they wanted to win. He played the game the right way,” Clarke told the Nine Network.

Australian Olympic Committee president John Coates said he had long admired Benaud “as a player and as a leader of men”.

“And like all Australians I marvelled at his knowledge and love of the game as a commentator. He was a thorough gentleman,” Coates said in a statement.

Benaud played 63 Test matches between 1952 and 1964, becoming the first Test cricketer to take 200 wickets and score 2000 runs.

Renowned as a shrewd tactician, Benaud never lost a Test series while captain.

But for all his on-field achievements, Benaud’s ever-lasting imprint on the game he loved came off the field.

The Penrith-born Benaud was a key figure in the formation of World Series Cricket in the 1970s and was one of the world’s most recognised commentators, anchoring the Nine Network’s cricket coverage for decades.

CA’s chairman Edwards said Benaud’s passing “marks a profound loss to our nation”.

“Richie stood at the top of the game throughout his rich life, first as a record-breaking leg-spinner and captain, and then as cricket’s most famous broadcaster who became the iconic voice of our summer,” Edwards said.

Benaud was a mainstay in Nine’s cricket coverage until the past two summers – a car accident in 2013 sidelined him before he announced in November last year that he was fighting skin cancer.

He did, however, manage to voice a touching tribute to Phillip Hughes, who died when struck by a bouncer last November, which was screen before Australia’s Test series against India last December.