Petersen, a sheep and beef farmer and former chairman of Beef and Lamb New Zealand, said local producers should not be disadvantaged by Britain's decision to exit the EU trading bloc.
"It's a message that we are hearing from the leadership in the UK - including [trade secretary] Liam Fox," he said. "This is a consistent message and one that we certainly welcome," he told the Herald.
When Britain does finally exit the EU - expected to be around March 2019 - New Zealand will require a trade deal with Britain and a separate one for the 27 remaining EU countries.
The New Zealand wine and sheep meat trade into Britain is significant, and New Zealand horticultural products are increasingly making their presence felt in EU markets.
"We keep reinforcing that whatever the agreements that we end up agreeing, the key principle is that New Zealand should not be any worse off," Petersen said. "Under the World Trade Organisation, that is a very important principle."
At today's news conference, Johnson said that Brexit would not be about Britain turning away from the world.
The bilateral talks in Wellington focused primarily on post-Brexit challenges, in particular a swift conclusion of a free trade agreement once Britain had quit the EU, and the rights of Kiwis to travel to and work in the UK.
Asked how he would appease British farmers who were wary about such a deal, Johnson said "no one is going to be any worse off".
"We already are the proud and grateful recipients of a lot of New Zealand sheepmeat and indeed butter. I think my grandmother would buy absolutely nothing else but Anchor butter, I want you to know."
He dismissed a suggestion that infighting within his Conservative Party could undermine any progress towards a free trade deal in the two years before Brexit took place.
In his opening remarks, Johnson praised the closeness of the British and New Zealand governments, saying there was a "total failure to disagree on any point of substance" on trade, security or other issues.
"These are two countries which really do think on the same lines on so many views that matter to our people and to our electorates," he said.
The UK is the second biggest market for New Zealand wine, after the United States, and is worth just under $400 million a year.
New Zealand sends about 200,000 tonnes of sheepmeat to Britain and the EU each year, and Britain remains a significant market for New Zealand lamb.
Dean Hamilton, chief executive of New Zealand's biggest meat exporter, Silver Fern Farms, said the UK was an important market for lamb.
"It was pleasing to hear UK Foreign Secretary Boris Johnson's reassurance that sheepmeat producers would not be worse off post-Brexit," Hamilton said.
"We are very supportive of our country's trade negotiators and their ability to build a constructive and mutually beneficial trade agreement with the UK."
(additional reporting Isaac Davison)
