Asked whether Chief of Defence Lieutenant General Tim Keating had raised similar concerns about Iraqi soldiers at Taji, Mr Key said he had not.
Labour's defence spokesman David Shearer said Mr Carter comments reinforced fears about Iraqi forces' leadership and supply of resources.
"You can do all you like training them to shoot straight as we are doing, but the real problems lie further up the chain."
Ministers also reaffirmed that the risk assessment in Iraq had not changed as a result of Isis' advances in Iraq and Syria.
Mr Key, who confirmed that he planned to visit Camp Taji this year, said: "I've checked with our defence people and my national security people and both of them advise me that there's no reason to change our thought processes on the risks that our people face in Taji.
"Like any deployment that we make ... there's a thorough process that we go through, there are officials that meet and there are early warning systems of making sure that if the situation needs to be reviewed it will be reviewed.
"But none of those have been triggered and at this point there's no likelihood they'll be triggered."
The risks to the New Zealand deployment were not judged on Isis' proximity to Taji, but on whether there was an "absolute threat" to the troops' safety.
Mr Key said the NZDF reserved the right to change its mission. This has previously occurred in Bamiyan, in Afghanistan, when soldiers were given approval to extend their patrols into neighbouring regions to intercept insurgents who had killed two New Zealand soldiers.
Defence Minister Gerry Brownlee would not comment on whether the NZDF had an emergency evacuation plan or what might trigger an evacuation.
But he said potential evacuation would have been considered during the initial security assessment of Camp Taji by New Zealand officials.
Asked whether the troops could be withdrawn earlier than the proposed two-year timeframe, Mr Brownlee said he would not speculate on any potential changes to the mission.
"This is a war situation. We are training people to be leaders in that war and clearly you're going to get a lot of activity that will be to and fro in that regard."
Mr Key said New Zealand was capable of evacuating its own troops urgently without assistance from US or Australian forces.
Labour leader Andrew Little said he had concerns about the lack of detail about an exit strategy for New Zealand troops.
"It is important, I think, that Government reassures New Zealand that there is a way of keeping our troops safe and secure, and if that means extracting them at whatever time, that they can do that as well."
