Richie Benaud's family held a private funeral for the former Australian cricket captain and commentator on Wednesday.

The country's prime minister Tony Abbott offered a state funeral to Benaud's family, but his wife Daphne declined.

Benaud, who became the first player to score 2,000 Test runs and take 200 Test wickets, died peacefully in his sleep last Thursday at the age of 84 after battling skin cancer.

According to the Daily Mail, former Australia players Shane Warne and Ian Chappell attended the service, while Benaud's former teammate Brian Booth spoke during the funeral.

The intimate service was held at the Eastern Suburbs Memorial Park.