Senator Nash and Senator Xenophon were the last of seven federal politicians to admit they were dual citizens, as the citizenship crisis swept through Canberra.
Section 44 of the constitution stops foreign nationals from being elected to federal parliament.
In submissions to the High Court, Solicitor-General Stephen Donaghue QC said the Commonwealth had obtained legal advice from a British QC that Senator Nash was indeed a British citizen at the time of the last election.
Mr Donaghue said the Commonwealth understood that "conclusion will not be disputed".
Senator Nash admitted to Parliament she had discovered she was a British citizen through her father, who was born in Scotland.
Acting on behalf of the Attorney-General, Mr Donaghue said the Commonwealth had sought advice from the same British QC in relation to Senator Xenophon.
He also offered to obtain advice from Greek and Cypriot legal experts about Senator Xenophon's privileges under their respective citizenship regimes.
Senator Xenophon admitted he was considered to be a UK Overseas Citizen, as his father was born in Cyprus when the Mediterranean Island was still a British colony.
Nash, Joyce draw Labor's ire for remaining in ministry
The five other cases — Deputy Prime Minister Barnaby Joyce, former Nationals minister Matt Canavan, One Nation Senator Malcolm Roberts and former Greens senators Scott Ludlam and Larissa Waters — were heard for the first time in Brisbane last month.
At the time, Mr Donaghue said the Commonwealth was dealing with the five cases in two categories.
He said Mr Joyce, Senator Canavan and Ms Waters would have had no knowledge they were considered citizens of New Zealand, Italy and Canada respectively.
But the Solicitor-General argued the cases of Senator Roberts and Mr Ludlam were different, and they ought to have been aware.
Labor has criticised Senator Nash and Mr Joyce for remaining in the Turnbull ministry while their eligibility for Parliament remained uncertain.
Prime Minister Malcolm Turnbull maintained he was confident the High Court would rule in favour of his Coalition colleagues.
The High Court will hear the full arguments in the seven cases on October 10-12.