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 Mr Key's comments did not reflect the good working relationship between New Zealand and Hungarian troops.
"The territories are separate responsibilities of each country and how things work between the two PRTs are dealt with at a local level.
"Maybe there's a gap there that needs to be addressed, but it'd be dealt with at that level and not by making snide remarks and inferring blame on Hungary for two New Zealanders' deaths.
"It's completely unhelpful because I'm sure there's very good reasons why Hungary doesn't [patrol at night].
"If New Zealand feels it is necessary to do that, then it is a discussion which should already have started."
She added: "I felt quite offended by it. It's ... emotive, quite derogatory. That's my personal opinion.
"It probably, if anything, just reflects more on John Key than on the actual relationship between New Zealand and Hungary."
Ms Szentirmay said the Hungarian PRT was willing to assist in helping to stop insurgent attacks.
Mr Key said yesterday that New Zealand would not apply diplomatic pressure on Hungary to police the border region of the Baghlan Province.
Victoria University professor of strategic studies Robert Ayson said he was "not 100 per cent surprised" by Mr Key's comments, given that Hungary's role in Afghanistan had been criticised before.
"It reflects the fact that different countries in their different PRTs have got various rules of engagement. Some are more permissible than others. Probably on the whole New Zealanders tend to ... be able to write broader rules of engagement."
But he said the primary concern should not be other countries' operations but the capabilities of the Afghan national forces, which are expected to take over security when New Zealand withdraws from Bamiyan Province late next year.
He said that even if the wider patrols improved security for New Zealand troops, it still amounted to an expansion of the Defence Force's role at a time when it should be trying to reduce its responsibilities.
Mr Key confirmed this week that the PRT was still scheduled to withdraw in 2013.