Prime Minister Jacinda Ardern stripped Ms Curran of her open government and digital services roles and dropped from her Cabinet last month after Ms Curran failed to disclose a meeting when answering a Parliamentary Question about her appointments.
Parliament met yesterday for the first time since Ms Curran's demotion on August 24.
Speaker Trevor Mallard agreed to National's request for an urgent debate on Ms Curran's removal from Cabinet.
''Clare Curran should have been stripped of her warrant, stripped of all ministerial responsibilities, and no longer be in this Parliament as a minister,'' Mr Bridges said.
''Despite the rhetoric of transformation ... and the most transparent Government ever - what have we got?
''Their minister of, quote, 'open government' has been sacked for her complete lack of transparency and openness in relation to all things: secret meetings, secret mobile phones, and secret emails.''
Leader of the House Chris Hipkins defended Ms Curran, saying
''she is a good friend of mine, and I believe that she's doing a good job.''