Union leader Paul Howes' call for the ALP to move to a binding vote in support of same-sex marriage has been rejected by Labor's potential leaders.

On Wednesday, both leadership hopefuls Anthony Albanese and Bill Shorten, as well as interim leader Chris Bowen, argued the Labor Party should stick with a conscience vote.

While they both support same-sex marriage, Bill Shorten and Anthony Albanese disagree that there should be a binding vote on the issue within Labor. Credit:Rob Homer

In a morning radio interview, Mr Howes argued that Labor had to go one step further on same-sex marriage.

''It's very clear that a conscience vote is a nonsensical position for Labor to adopt and a conscience vote will never allow this important last step of reform in removing all forms of discrimination against people in same-sex relationships to be achieved,'' he told ABC Radio.