Prime Minister Tony Abbott says Australia is not likely to become a republic any time soon, with his government having "bigger things" on its mind than Australia's head of state.

Mr Abbott, a constitutional monarchist, has moved to cast a fresh push for a republic as a peripheral issue after Treasurer Joe Hockey was named as co-chair of a bipartisan parliamentary friendship group with Labor senator Katy Gallagher to revive the debate.

The Prime Minister said he and Mr Hockey had not discussed the group before it was announced by head of the Australian Republican Movement, and Mr Hockey's friend, Peter FitzSimons at the National Press Club on Wednesday.