Two of the biggest right-wing unions have swung their support behind Chris Minns for the NSW Labor leadership.

The Health Services Union  and the Shop Distributive and Allied Employees' Association  will back Mr Minns for the leadership over his contender Jodi McKay, believing he has the best chance of winning the election.

The move is seen as significant within the party's senior ranks, as Ms McKay is the preferred candidate of the party's Sussex Street head office, led by general secretary Kaila Murnain.