The Turnbull government will need crossbench support to follow through on its threat to send Labor MPs under a citizenship cloud to the High Court.

And the opposition is warning of "nuclear" retaliation if the government does pursue its MPs, saying it will target the Coalition's "foreign five".

Malcolm Turnbull says the pressure is now on Bill Shorten. Credit:AAP

Prime Minister Malcolm Turnbull last week threatened to use the government's slim majority in the lower house to refer as many as four Labor MPs - including Justine Keay and Susan Lamb - to the court because they were officially still dual citizens when they nominated as candidates.

Labor argues they are in the clear because they took all reasonable steps before the election to renounce their foreign ties, but the Coalition believes they could be ineligible given the court's strict judgement against five MPs - including former deputy prime minister Barnaby Joyce - last month.