A citizenship crisis that robbed Australian Prime Minister Malcolm Turnbull of his one-seat majority will claim another politician, with the Senate president on Wednesday saying he will resign after confirming he was a dual national.

Stephen Parry, the leader of the upper house and a member of Turnbull's Liberal party, said he will submit his resignation on Thursday after he being told that along with his Australian citizenship he also held British citizenship by descent.

Parry's father was born in Britain before moving to Australia as a boy in 1951, which automatically gave Parry citizenship by descent.