Asked about the claim that Hungarian troops did not patrol after nightfall, Mr Key said: "As far as I'm aware, the Hungarians don't go out at night. Not in Afghanistan anyway - they might in Budapest.''
Honorary Consul-General of Hungary Klara Szentirmay said after the comments that they did not reflect the good working relationship between New Zealand and Hungarian troops.
Mr Goff said Mr Key's comments were ill-considered and had prejudiced New Zealand's international relations with Hungary.
"The real irony was that the request was turned down on the grounds that releasing it would prejudice the international relations of New Zealand.
"John Key's disparaging remarks were widely reported in Hungary. His reflections on the courage of that country's soldiers caused a level of public anger that would only have been topped in New Zealand if someone had said the same of our troops.''
Mr Key did not apologise for his comments.
"Slights like these are long remembered. They are hugely damaging to our international relationships and won't help New Zealand's bid for support for election to the UN Security Council in 2014,'' Mr Shearer said.