The opposition has received legal and parliamentary advice on a range of decisions which could be challenged after the High Court disqualified Mr Joyce and Ms Nash from parliament.
"The first thing I want to say is that I want to thank the people of New England for the support I have been receiving, overwhelming support", he said.
Mr. Joyce will be able to stand for re-election, however, having renounced his New Zealand citizenship since the last election.
It comes after a High Court ruling found five members of the house and Senate had been inelligble for election due to dual citizenship provisions, including now former deputy prime minister Mr Joyce.
Australia's government - which is clinging to power by a single seat - has been plunged into crisis after a court disqualified the deputy prime minister from parliament, ending its parliamentary majority.
Draymond Green compares Texans owner Bob McNair to Donald Sterling
17 meeting, Houston Texans owner Bob McNair remarked: "We can't have the inmates running the prison" in reference to the players. An ESPN report published Friday detailed last week's conference in NY , saying McNair's comment "stunned some in the room".
Mr Joyce fired a shot against those providing "off the record" comments about the Nationals.
Mr Joyce has chosen to fight for his former seat and has begun campaigning in New England ahead of a by-election on December 2.
He has also sent a public warning to Liberal backbenchers who have anonymously criticised the Nationals in the media over their citizenship woes, saying his party was the reason the Coalition was in government.
But the court found Mr. Joyce was a New Zealander by descent at the time of his nomination previous year.
Independent MP Cathy McGowan and NXT MP Rebekha Sharkie have indicated they will back the government in a no-confidence motion.