Mr Dunne, a minister and the leader of United Future, described Mr Hammond as a "patronising figure from abroad loftily telling us we are in the club, we are part of the family and it would be lovely to have you along for the next round of unmitigated slaughter".
He said the debating chamber had plaques on the wall of other times "the family" had acted together.
"Gallipoli, the mindless slaughter of Australian and New Zealand troops in the pursuit of a British objective, Passchendaele and the Somme, so to come here and say to New Zealanders today 'we love having you on board, you are part of the family but you've still got to queue up at the aliens gate at Heathrow' is unacceptable in the extreme."
New Zealand First leader Mr Peters said Mr Key's concern was to be in the club - "the club that says that if you go to Australia and you work there for 21 years and you get tipped out of your job you do not get the dole any more ... Or is it the club with the United States, which says: "We'll give a free trade agreement to Chile and Morocco but we won't give one to New Zealand."
Mr Little, the Labour leader, said everybody felt the urge to do something but: "After 10 years of training of the Iraqi Army by the ... best-resourced army in the world, what is it that we can do now that is going to make a difference?"