​Prime Minister Malcolm Turnbull has ruled out chasing down who leaked a photo of the public servant at the centre of the Jamie Briggs saga, but condemned the former minister who initially distributed the image.

Four days after Mr Briggs resigned as cities minister for inappropriate behaviour towards a female diplomat in Hong Kong, a pixelated photograph of her was published in weekend newspapers, alongside private text messages to Mr Briggs' chief of staff Stuart Eaton and her age and job description.

The leak - seen as an attempt to discredit the woman - prompted calls for Mr Turnbull to launch an inquiry.