New Zealand's Prime Minister says the desecration of Commonwealth war graves in Libya is a shameful act of violence.
Libya has apologised after armed men smashed the graves of British and Italian soldiers killed during World War II.
Amateur video footage of the attack posted on the social networking site Facebook showed men kicking over headstones at the Commonwealth War Cemetery and using sledge hammers to smash a metal and stone cross at the weekend.
One man could be heard saying: "This is a grave of a Christian" as he uprooted a headstone.
The incident happened in the eastern city of Benghazi, near where British and Commonwealth troops fought heavy battles against German and Italian forces during World War II.
New Zealand's Ministry of Culture and Heritage says 11 New Zealanders are buried at the cemetery, but it is not yet known whether their graves have been damaged.
Mr Key says the attacks are distressing and if there is any damage to the New Zealand graves the Government would want to see them restored.
Watty McEwan, a New Zealand veteran of the North Africa campaign,
told Radio New Zealand's Checkpoint programme on Monday the people behind the attack are ignorant and must be punished.
"Have they caught the perpetrators and will they punish them the same as they would if they had desecrated one of their religious idols or graves of one of their Libyan heroes?
"They should punish them who have insulted our dead."
Mr McEwan says the soldiers' remains should be exhumed and shifted in the wake of the attack.
New Zealand Returned and Services Association national president Don McIver says surviving veterans of the campaign will be devastated by the incident.