Police also said they were keeping tabs, and Waitakere police spokeswoman Rebekah Holt said: "We don't recommend you try this at home."
The story made headlines in at least 22 overseas publications, in countries as diverse as England, Australia, South Africa, the United States, India, France and Scotland.
The Guardian newspaper ran a story on the front page of its website saying "don't worry about Russia's bioweapon laboratories and North Korea's nuclear programme: the greatest threat to world security is sitting in a shed in New Zealand".
The newspaper quoted the editor of Jane's Missiles and Rockets as saying Mr Simpson's device would not be a serious security risk because it would be unable to beat defensive systems.
Air Force staff in New Zealand have refused to comment on whether defence systems here could stop the missile, which Mr Simpson hopes will be able to fly 100km in 15 minutes.
Libertarian Party spokesman Robert Palmer said Mr Simpson had provided "the first credible defence system in this country since Helen Clark and [Defence Minister] Mark Burton gutted the Air Force".
Mr Palmer said New Zealand's Defence Force "has been bested by a backyard mechanic".
Mr Burton's staff referred calls back to Mr Seward.
An exhausted Mr Simpson said yesterday that he had just finished interviews with three Australian and New Zealand television channels and "about a dozen radio interviews with stations from as many different countries".
One controversial aspect of Mr Simpson's project is that he is posting details of the missile's construction on a website.
Terrorism experts are divided over whether the site encourages terrorism or merely serves as a warning that the technology for such weapons is widely available.
Mr Simpson hopes to have the missile working within a month.
He said he would ask the Air Force to help him fire it.
Boffin builds backyard missile
Herald Feature: Terrorism
Related links