''I don't agree with people taking the law into their own hands, and threatening babies is the lowest of the low,'' she said.
Federated Farmers and Fonterra received anonymous letters in November.
Packages of milk powder, later testing positive for a concentrated form of 1080, accompanied the letters.
The letters contained a lethal dose of 1080 and carried a threat to contaminate infant formula milk unless New Zealand stopped using 1080 for pest control by the end of March.
Prime Minister John Key and Primary Industries Minister Nathan Guy called the threats acts of ''eco-terrorism'' yesterday.
At a hastily called news conference in Wellington, police said the letters were likely a hoax, and carrying out the threat would be impractical.
They said a threat to carry out ''a publicity campaign promoting the actions of the threat-maker'' was also received.
Ms Sawyer also said the situation raised a series of questions.
''Why on earth have they taken from November to release the letter? ... And who has access to pure 1080? It's a highly deadly poison in its pure form; it should be kept under lock and key.
''It's extremely worrying if someone's flinging pure 1080 around. It's not something that should be available to anybody, really.''
Otago Federated Farmers president and dairy farmer Stephen Korteweg described the threat as ''sickening'', particularly as it involved baby formula.
If those involved were ''so brave'' to be making such a statement, ''why don't they just come out and say it?'', Mr Korteweg said yesterday.
It is not known why a March 31 deadline was chosen.
An Auckland-based criminal investigation - Operation Concord - began in November and involved up to 36 police personnel. Police urged the person or people who made the threats to reveal themselves, and asked the public to help.
''You might be aware of someone who has strong views [about] 1080 and has made threats,'' deputy commissioner of national operations Mike Clement said yesterday.
''The letter writer may not have really considered the implications of their actions when this communication was drafted,'' Mr Clement added.
Police were treating the threats as a ''crime of blackmail'' rather than terrorism.
No particular brand or company's formula was targeted.
The threat was designed to spark fear ''in order to generate a domestic policy outcome,'' Minister for Primary Industries (MPI) deputy director-general Scott Gallacher said.
He said similar threats were occasionally made abroad but the November letters were the first of their kind in New Zealand.
Mr Gallacher said New Zealand's trading partners were told in recent weeks of the threat, and responded calmly and with gratitude for an ''up-front'' Kiwi approach.
Fonterra chief executive Theo Spierings called the threat ''a despicable act against New Zealand''.
Mr Guy learnt of the letters in November, as did associate minister Jo Goodhew.
Mr Guy said authorities deployed a ''whole of Government'' approach in response.
Police, MPI, and the ministries of Health, the Environment, and Foreign Affairs and Trade were among groups involved.
Mr Guy said 40,000 tests were carried out on infant formula and other formula in recent weeks and 20 manufacturers contacted.
No traces of 1080 were found in any of the tested products, Mr Guy said.
''We are confident that New Zealand infant and other formula is just as safe today as it was before this threat was made. People should keep using it as they always have,'' he said.
The ability for anybody to deliberately contaminate infant and other formula during manufacturing was ''extremely low'', he said.
Authorities went public with the threat after fielding media inquiries. Major supply-chain players, including retailers, already knew of the threat.
Synlait Milk managing director Dr John Penno said the company's food safety systems and security standards had been specifically designed to protect against such threats.
Expatriate Beijing business adviser David Mahon last night said news of the threat had barely registered in Chinese media.
''There's one food industry website that has noted it but it's not in social media or mainstream media,'' he said.
He has advised numerous New Zealand firms, including dairy exporter Fonterra, on entering the Chinese market.
''Tomorrow some translations of what's been in the New Zealand press will be posted here, but it's unlikely to run,'' he told BusinessDesk from Beijing.
''The Chinese Government, that has quite a control over even social media, would probably shut it down and stop its progress. It will be seen for what it is, which is a crank of some form.
''The Chinese Government does have confidence in New Zealand's supply chain in dairy.
"Its problems have been more about the bungling of communications around botulinum [the 2013 false scare over botulism contamination] and to some extent DCD [in 2012, involving a nitrate uptake inhibitor used on grasslands].
"There's been no major scandal relating to Fonterra having contaminated product so I don't think there is an issue.''
The NZX put a trading halt on all dairy companies yesterday afternoon. Units of the Fonterra Shareholders' Fund fell 0.9% to $5.80 when trading resumed and Synlait Milk fell 3.4% to $2.85. Trading was also halted in the NZX Dairy Futures and Options market.
Supermarket giant Foodstuffs (New World, Pak'n Save, Four Square) released a statement saying formula purchased from its stores is safe, and there will be increased security in its stores to ensure that.
Progressive Enterprises (Countdown, Fresh Choice, Supervalue) also said it had put in additional security.
Infant formula was being moved behind service counters.
- Staff reporters & NZME
Contacts and advice
• Parents with any concerns could call Plunketline (0800 933-922) or Healthline (0800 611-116) for advice.
• The Ministry of Health said anyone who suspected tampering could phone 0800 723-665.
• Anybody who suspected their formula had been tampered with could also take it to their nearest police station.
• If cans or bottles of formula had tears, rips, holes, punctures or noticeable bulges, it was possible the product had been tampered with.
• Visit www.foodprotection.govt.nz for more advice on how to check packaging for signs of tampering, and for information about the Government's response to the threat.
• Those with information about the threats should call Operation Concord team on 0800 723-665, or Crimestoppers on 0800 555-111.
