Shorten said the Government had failed to explain why another cabinet minister Matt Canavan, who has also been referred to the High Court over his eligibility, had stood aside while Mr Joyce had not.
Conservative senator Cory Bernardi has called for the Parliament to be suspended until the crisis can be resolved, the Sydney Morning Herald reported.
Meanwhile, Treasurer Scott Morrison said Labor had been "sneaky" in working with NZ Labour colleagues to undermine Joyce. It was revealed this week an NZ Labour MP had asked a question in the New Zealand Parliament about a scenario similar to that of Joyce.
The query came after he discussed the citizenship issue with a staffer of Labor senator Penny Wong.
"Rather than come into the parliament and raise these questions, what they have done, in a very sneaky way, is run around over there in another country and try and dredge this stuff up," Morrison said.
Labor MP Rob Mitchell brandished a tinfoil hat, telling reporters Foreign Minister Julie Bishop - who championed the conspiracy argument in Parliament - had lost the plot.
Media inquiries had already been under way when the NZ MP raised his query. Another minister, Michael Keenan, rejected media reports he held dual nationality, insisting he renounced his British ties in 2004 before he entered Parliament.
Fairfax Media had reported Keenan may be a British citizen courtesy of his father Peter, who was born in England in 1943 and emigrated to Australia, where he married.
- AAP