LABOR'S Left faction will demand an increase in the amount of money raised by the proposed mining tax, a challenge to the authority of the Gillard government's leadership.

It is part of a broader new thrust by the Left to move the government towards what it calls "a more egalitarian society".

Labor Senator and convener of the party's Left faction, Doug Cameron.

"We should have another look at whether the mining industry is paying its fair share, and whether the community is getting a fair outcome from it," a national convener of the Left, Doug Cameron, told the Herald.

He said the issue would be on the agenda for Labor's national conference, notionally the party's supreme policymaking body.