Another Australian lawmaker has announced his resignation over a constitutional ban on dual citizens sitting in Parliament, triggering a second by-election that could cost the government its fragile grip on power.

John Alexander announced on Monday that he was waiting on advice from the British Home Office on whether he had inherited citizenship from his English-born father. On Saturday, the 67-year-old former professional tennis player told reporters he was "most likely" a dual citizen.

Deputy Prime Minister Barnaby Joyce is contesting his seat at a by-election in December after the High Court disqualified him because he had inherited the citizenship of his New Zealand-born father. Joyce immediately renounced his New Zealand citizenship.