Neither Barnaby Joyce nor Matt Canavan will contest the fact they are dual citizens under New Zealand and Italian law, according to the solicitor-general Stephen Donaghue QC.

That means the only issue that will be debated is whether that rules the pair ineligible to sit in Parliament under an interpretation of section 44(1) of Australia's constitution.

The nation's chief counsel also said the Commonwealth is ready to step in and give the High Court legal advice on the citizenship status of the other parliamentarians awaiting a decision on their fate.

But if those other parties, such as One Nation's Malcolm Roberts, do not agree with the advice the Commonwealth gets from lawyers overseas, they can get their own, but risk delaying any judgement on their case.

Acting on behalf of the Attorney-General, Mr Donaghue has filed submissions to the High Court on five parliamentarians who have had their alleged dual citizenship referred by Parliament for judgement.

Mr Donaghue has suggested the cases should be heard by the court on September 13 and 14 — a quick turnaround because they relate to the current makeup of the Parliament.

"The Attorney-General submits that there is a compelling public interest in the references being determined as quickly as possible," Mr Donaghue said.

Another two senators, Nationals deputy leader Fiona Nash and South Australian Nick Xenophon, will have their citizenship status referred to the High Court when Parliament returns next month.

Mr Donaghue said he understood lawyers for Mr Joyce and Senator Canavan will not dispute the fact that under New Zealand and Italian law respectively, they are citizens of foreign countries.

The first hearing of the matters will be held this Thursday in Brisbane.

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