"And of course they believe we are in the class of infidel and are quite happy to destroy things, including human life in our own country. So we have a reason for being there and as long as that is alive we will have to, through our reviews, consider our ongoing involvement."
New Zealand has set a two year limit on its deployment with a review after one year - that will take place in February.
A further rotation of troops is expected in later October or November.
Mr Andrews said Australia would review its commitment every year but did not have a set end point.
Mr Brownlee refused to give explicit support to Australia's decision to start air strikes in Syria but did give a tacit nod, saying said it could help to cut back Islamic State activities which would make the task of Iraqi forces fighting them easier.
While New Zealand's role is restricted to the 145 troops at Taji on the training mission, Australia is also working with United States on air strikes in Iraq and, more recently, Syria.
Mr Brownlee said New Zealand could not take part in air strikes itself because it has no strike force and had no position on it, either in support or against.
"But while we are together in Taji we are in a common way saying we want to improve the chances of the Iraqi security forces getting rid of Daesh out of their country. Given a lot of it comes from the eastern part of Syria, this may well retard some its activities."
Mr Andrews defended the decision to expand air strikes to Syria, saying the Islamic State presence in Syria was a risk to Iraq and justified on the basis of defending Iraq.
He said Australia had no intention of sending troops into Syria on the ground, saying it was in Iraq at the Iraqi government's invitation.
Asked if he believed New Zealand could expand its role as regards Syria, he said it was a sovereign country and Australia respected its right to make its own decisions.
Australia has about 300 troops at Taji who are working alongside the 145 New Zealand troops in a training mission for the Iraqi soldiers which have so far trained about 1600 soldiers between them.
Mr Andrews said those soldiers were now out in the conflict and initial reports were that the training had been effective.
Australia is also reducing the number of special forces it has in Baghdad working with Iraqi special forces from 170 to 60, which Mr Andrews said was partly because of the Taji deployment as well as mission fatigue.
"Our special forces have been on a very high tempo of operations for over a decade now, so we want to make sure we are in a position that we don't effectively wear them out."
While Mr Andrews was happy to discuss the battle in Iraq, he was less happy to talk about the recent battle in his own party in Australia.
Mr Andrews faces losing the portfolio after last week's change of leadership from Tony Abbott to Malcolm Turnbull, but Mr Andrews refused to comment on that or his previously voiced support for Mr Abbott.
He sought refuge in what he said was the convention that ministers travelling overseas did not discuss domestic politics.
