Trade Minister Tim Groser says there have been glimmerings of movement on improved assess for dairy products at the latest Trans-Pacific Partnership talks, but not enough to satisfy him.
Mr Groser is in Atlanta trying to win key concessions for New Zealand, and has previously said that current offers to open up access to dairy markets were completely inadequate.
Mr Groser and his 11 counterparts are negotiating in the proposed Pacific-wide trade pact to find agreement on sensitive matters such as dairy, cars and medicines.
The government has retreated from its earlier insistence on a high quality deal, but Mr Groser said he was yet to see offers of commercially meaningful access for dairy from the other countries.
He said a deal could be successfully concluded this week, but that did not mean it would happen.
New Zealand's agricultural trade envoy Mike Peterson had earlier said there were some positive signs that people wanted to close the deal, but there needed to be movement right across the board on dairy.
"It's not just a Canadian issue, and I think the reality is that if we're going to get movement on dairy, it will actually be across all of the markets that we're looking into here, and the TPP member countries, and that's still quite a big ask."
However, Prime Minister John Key told Reuters on Wednesday that he saw a good chance of wrapping up the deal this week but warned political headwinds may scupper the pact if negotiations dragged on too long.
Mr Key told the Asia Society in New York, New Zealand was still not happy with dairy market access but agreement was closer on other tricky matters, including intellectual property.
Compo for Canadian dairy farmers
Canadian dairy farmers, meanwhile, have been assured they will get government compensation for any losses resulting from a TPP deal.
Farmers parked dozens of tractors in central Ottawa and walked their cows down the main street opposite Parliament this week after reports Canada was preparing to accept more American milk, without getting reciprocal access for Canadian dairy farmers in the US.
Agriculture Minister Gerry Ritz has told a debate in the lead-up to Canada's federal election later this month that while he did not rule out allowing more imports, farmers would be compensated for losses.