Those claims have been picked up by overseas media including The Guardian. But Ayson said he didn't think there would be "hordes of people watching this with particularly close interest beyond New Zealand".
"You just never know - you do not know what triggers or precipitates violent action. Is there a possibility of some effect? Yes. But I think on the whole...I doubt it would be top of my list for things that change the risk profile for New Zealanders."
Meanwhile, New Zealand politicians addressed the attack on Westminster, with Prime Minister Bill English saying New Zealanders' links with London made it feel "very close to home".
In Parliament, Deputy Prime Minister Paula Bennett moved a motion condemning the attack and expressing condolences to the friends and family of those killed and injured.
"An attack that strikes at the heart of democracy and the United Kingdom strikes at the heart of democracies everywhere," Bennett said.
Labour's deputy leader Jacinda Ardern also expressed condolences.
"In moments like these it is hard to not reflect on the very personal relationship this House and many of us will feel as a Westminster democracy, with long-standing ties to the United Kingdom.
"But it is much more personal than that - London is a place where many of us have lived, have worked, and where we still have both friends and family.
"My sister was in the city yesterday, her first thought like many Londoners was to immediately reassure her family abroad that she was safe and to carry on. And that is what London has always done."