Police say there is no evidence any of the men arrested for suspected terrorist activities in Australia have ever been to New Zealand or have links here.
NZ's terrorist alert remained low yesterday - below Australia's medium risk warning - despite the arrests across the Tasman.
However, an anonymous internet claim that there is a threat to the Australian High Commission in Wellington next Tuesday is not being dismissed, although its authenticity can not be judged.
The Australians are due that day to co-host a function at Parliament for new MPs.
Parliamentary security told the Herald details about precautions would not be made public.
However, it was usual for security to be discussed with hosts before a function was held.
A spokesman for the Australian High Commission, Paul Irons, said it did not comment on security issues.
Assistant Commissioner Peter Marshall said there was no evidence or information to suggest there was any threat to any establishment or organisation in New Zealand.
"However, we will thoroughly examine any current and ongoing information to maintain vigilance against any possible threat to New Zealand security," he said.
New Zealand police in Australia were in contact with their federal counterparts there.
Prime Minister Helen Clark had also been updated by police, and told there was no evidence or intelligence of any New Zealand links to those arrested.
However, it remains unclear if New Zealand will re-examine its counter-terrorism laws as both Australia and Britain have done since this year's London and Bali bombings.
Already New Zealand has tightened immigration and customs laws, and it has the power to detain without charge a person considered a national threat, as it did with Algerian politician Ahmed Zaoui.
His security status remains unresolved almost three years after he arrived here and claimed refugee status.
While civil liberties groups are nervous about possible increased counter-terrorism laws, police counter-terrorism expert Assistant Commissioner Jon White has indicated New Zealanders might need to debate the balance between lost personal freedoms and security.
NZ alert level still set at low
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