Mr Key said he had had no specific advice to suggest such an attack in New Zealand was likely.
"But there is always increased risk when you have these sort of public events and that is just the stock standard advice I get whether it is the co-hosting of the Cricket World Cup or a Rugby World Cup or a significant event like Anzac Day."
However, he did not think it was a good idea to stay away.
"If people stay away, you are giving in to the threat of these terrorists."
Mr Abbott was in New Zealand for the dedication of Australia's contribution to Pukeahu, the new National War Memorial Park in Wellington at the tomb of the unknown warrior.
Mr Abbott said at a press conference it was fitting that 100 years on from Gallipoli, Australians and New Zealanders were again working together for shared values and interests in Iraq.
He was sure the New Zealanders in Iraq would be "splendid sons of Anzacs".
The themes of Gallipoli and the fight against Isis are set to converge later in the week when Mr Abbott and Mr Key speak at a peace conference in Istanbul before heading to commemorative events at Gallipoli.
They will have talks there with Turkish President Recep Tayyip Erdogan about Isis.
Mr Key said he expected he would thank Turkey for everything it was doing to try to limit foreign fighters crossing their borders to join Isis.
Mr Abbott was more blunt.
He said he would talk about what could be done "to better police that border to better ensure that people who have no reason to be going there are prevented from being there".
Mr Key will attend services at Gallipoli on April 24 and 25, including the dawn service, the New Zealand service at Chunuk Bair and the Australian service at Lone Pine.
Among Mr Key's formal New Zealand delegation will be former Prime Minister Helen Clark, Opposition leader Andrew Little, and the Chief of the Defence Force, Lieutenant General Tim Keating.
