The Turnbull government has been rocked by another day of drama over the dual citizenship fiasco, a diplomatic stoush with New Zealand and another Liberal MP facing questions over their eligibility for Parliament.

The government is moving closer towards unilaterally referring four Labor MPs to the High Court to have the validity of their election tested.

The move would mark a dramatic escalation of the citizenship stoush that has so far led five MPs - Barnaby Joyce and Matt Canavan (Nationals), Scott Ludlam and Larissa Waters (Greens), and Malcolm Roberts (One Nation) - to be referred to the High Court to have the validity of their elections examined.

The move to refer those four Labor MPs - Justine Keay and Susan Lamb (both with British heritage), Tony Zappia (born in Italy) and Maria Vamvakinou (born in Greece) - would force them to produce documents that back up the detailed explanations they have given that they say proves they have complied with section 44 of the constitution, which states that dual citizens cannot be elected to the Federal Parliament.