Hong Kong's Chief Executive Carrie Lam rejected the suggestion that she should allow a full independent inquiry into the police's handling of ongoing protests in the city state.

Since June last year, Hong Kong has witnessed violent protests triggered by a now suspended extradition bill that would have allowed people in the city to be sent to the mainland for trial. The public disorder has spread to consider other issues such as rampant property prices.

The most recent rally on Sunday once again turned violent and, not for the first time, media images appeared to show excessive force being used by police.

Lam told CNBC's Geoff Cutmore on Tuesday that police oversight was already stringent and that the force was acting in extreme circumstances.

"I certainly do not feel that with all these established mechanisms in place we should subject our police forces — which is working day in and day out to protect Hong Kong from all these criminal offences — to subject them to another sort of investigation," said Lam.