"We have to defeat them militarily and we have to defeat their arguments by proposing a counter-narrative, and that's what we are proposing to do as members of the anti-Isil (Isis) coalition."
The Iraqis were not asking for others to fight their war for them, he said.
"They are asking us to train people, to give them some strategic bandwidth to plan the campaign, to provide them with air cover.
"We know and they know that the ground war in Iraq cannot be won by foreign troops. It can only be won by Iraqis.
"Our job is to make sure that those Iraqis are as well trained and as well equipped as it is possible for them to be."
About 20 countries are taking part in a military coalition -- a subset of about 60 countries, including New Zealand, which are making some contribution such as humanitarian aid.
New Zealand's Cabinet was still awaiting reports from officials and discussions with Iraq on how best it could contribute to a training role, Prime Minister John Key said yesterday.
Mr Hammond said everyone had been shocked by recent terrorist events in Ottawa, Sydney, Paris and Brussels.
"If I may say so here in New Zealand, they remind us that nobody, however remote they are from the source of the terrorist action, is exempt or immune from this threat.
"We all have to work together to meet the challenge, which has most recently been expressed in the horrific murders of the Japanese hostages by Isil."
Mr Hammond prefaced his remarks by saying New Zealand and the United Kingdom were family with shared history and shared values.
It is the third visit in four years from a British Foreign Secretary, which was unprecedented contact, Mr McCully said.
Mr Hammond's predecessor, William Hague, visited twice.
The pair discussed trade and Mr Hammond said that as a good friend of New Zealand, Britain would act as "a champion" in the European Union for a EU-NZ free trade agreement.
He touched on China's growing economic and strategic power in the region.
"What we want to do is ensure that that power is expressed through a greater Chinese role within the rules-based international system that provides protection for our collective security and prosperity."