His decision was criticised by all the other major political parties except for Act.
But Rotorua National Party MP Todd McClay said New Zealand was not going to war.
Mr Flavell said there was a large scale humanitarian crisis in the Middle East, and New Zealand had much to contribute - "but not by sending our own troops".
Mr Flavell said his party understood the desire to assist in the fight in Iraq.
"Despite our views - we do wish our forces well - they will make us proud. We pray that they will be looked after and return home safe."
Mr Tabuteau did not support the decision, and said the Government had manipulated public opinion.
"It is a very sad day in Parliament. It's not so much their decision, it's the whole process to manipulate public opinion.
"They have no mandate from this government, they are a minority party in government, it's National taking the country to war."
"They did not engage with other political parties, it's been an absolute farce."
Mr Tabuteau was concerned New Zealand personnel would be involved in conflict.
"Saying it is non-combat is an evasive technique.
"The primary example is talking about support troops, when they are under enemy fire, what do we expect them to do? It's just a case of blatant manipulation."
Mr McClay said the mission to Iraq was to help the international coalition against the Islamic State of Iraq and the Levant (Isil).
"The Prime Minister has ruled out military force. This is part of our overall contribution to the international coalition of around 62 countries that are helping in various ways to fight this brutal and inhumane group.
"New Zealand is a country that stands up for its values.
"We stand up for what's right."