But it believes the five other politicians referred to the High Court - including Deputy Prime Minister Barnaby Joyce - should not be found ineligible.
The government believes only those who "voluntarily obtained, or retained" citizenship of another country should be affected by section 44 of the constitution which prohibits dual citizens running for parliament.
That does not include "a person who does not know that they are, or ever were, a foreign citizen".
The government's stance also gives hope to Nationals senators Fiona Nash and Matt Canavan and crossbench senator Nick Xenophon, who all claim they never thought they could be a citizen of another country by descent, and former Greens senator Larissa Waters, who is said to have not voluntarily acquired or retained her Canadian citizenship.
The government believes that the requirement to take "all reasonable steps" to renounce foreign citizenship doesn't actually require the person to take any steps.
"Taking no steps is reasonable in these circumstances," its submission reads.
In the submissions filed on behalf of Attorney-General George Brandis on Tuesday, the Commonwealth claims One Nation's Senator Roberts and Mr Ludlam - a former Greens senator - were incapable of being chosen to sit in parliament.
The High Court last week ruled Senator Roberts, who was born in India to a Welsh father and Australian mother, was a dual British and Australian citizen when he nominated as a candidate.
Mr Ludlam resigned in July after learning he was still a citizen of New Zealand, where he was born.
The Commonwealth believes Mr Ludlam and Senator Roberts voluntarily retained their status as citizens of New Zealand and Britain respectively and failed to take all reasonable steps to renounce it and should be disqualified.
Their vacancies should be filled by a special count, it submitted.
"The other referred persons are not disqualified," it said.
The matters will go before the full bench of the High Court on October 10.
