The coalition has failed to censure Penny Wong, as the government pressed its case that the Labor frontbencher's chief of staff connived with a New Zealand MP to undermine Barnaby Joyce.
The botched Senate attempt at censure - which attracted only the support of One Nation and Derryn Hinch - came at the start of a second day of government counter-attack over the scandal.
Mr Joyce was on Monday referred to the High Court to test whether his NZ citizenship by descent disqualifies him from sitting in parliament under section 44 of the constitution, which bans dual nationals.
On August 7, Fairfax journalists pursuing a story about Mr Joyce's citizenship status requested information from the NZ government.
About the same time, Senator Wong's chief of staff Marcus Ganley had informal talks with a friend, NZ Labour MP Chris Hipkins, about "domestic political issues including the section 44 debate", but she says no mention was made in the conversation of Mr Joyce.
Mr Hipkins decided on August 9 to ask a parliamentary question on notice to the NZ internal affairs minister whether a child born in Australia to a NZ father would automatically have NZ citizenship.
A day later, Mr Joyce was informed by the NZ high commission preliminary advice showed he was an NZ citizen - which was confirmed by NZ Prime Minister Bill English on Monday.
Attorney-General George Brandis told parliament on Wednesday Labor was involved in a conspiracy.
"It plainly crosses a line when a serious domestic political dispute ... is progressed by the opposition not through the process of the Australian parliament but through the process of a parliament of a foreign friendly nation," he told parliament.
Senator Wong said while it was "unwise" for her staffer to have engaged in the conversation, the NZ government had confirmed that media inquiries triggered a check of its citizenship records.
However, Foreign Minister Julie Bishop said only the NZ MP's question, not those from journalists, "put an obligation on the New Zealand government to act".
Former Liberal senator Cory Bernardi, who voted against the censure, said the Turnbull government had "overcooked" its conspiracy claims and appeared to be covering up its knowledge of the matter.
Mr Joyce defended his decision not to step aside as a cabinet minister, the course taken by his Nationals colleague Matt Canavan, who is also facing a High Court ruling on his eligibility to sit in parliament.
"If someone said to you 'you've got a firm case and a firm case to be in the clear', you continue on with your work," he told reporters, referring to legal advice from the solicitor-general.