The Turnbull government has suffered another embarrassing parliamentary defeat after the Senate thwarted its attempt to censure senior Labor frontbencher Penny Wong.

Attorney-General George Brandis sought to have the Senate censure Senator Wong over her alleged involvement in the revelation Deputy Prime Minister Barnaby Joyce was a New Zealand citizen when he stood for parliament.

Senator Wong has admitted her chief of staff was involved in fishing for information during a conversation with a friend from the NZ Labour Party.

The censure move was defeated 34-29 on Wednesday morning after the Greens and crossbenchers including the Nick Xenophon Team, Liberal Democrat David Leyonhjelm and former Liberal Cory Bernardi voted with Labor.

Earlier Senator Brandis accused Senator Wong of conspiring with a foreign political party to undermine the federal government.

"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 conceded it was "unwise" for her staff member to engage in that discussion but insists the questions about Mr Joyce's citizenship arose from media inquiries.

"It is incorrect to assert, as Senator Brandis does, that this story broke as a result of any action by my office," she told parliament.

The Greens dismissed the government move as "politics of distraction".

Senator Bernardi, who defected from the government earlier this year, said it was normal for people to exploit personal contacts for political gain.

"I challenge anyone in this place to say they would not have done the same," he told parliament.