The Morrison government's shot at making history by snatching a seat off the Opposition at the upcoming Eden-Monaro byelection has been dealt a blow by the Shooters, Fishers and Farmers Party, which plans to run a candidate and is tipped to preference Labor.

Confirmation of the Shooters' intent comes as the National Party pushes ahead with plans to also run, further splintering the conservative vote at the July 4 poll.