Stephen Harper begins a second Pacific Rim trip this month in New Zealand, a natural ally on nearly every topic except for Canada's heavily sheltered dairy industry, where the small country that's been dubbed the "Saudi Arabia of milk" is hoping regional free-trade talks will pry open Canadian markets.

The Trans-Pacific Partnership trade talks appear to be making progress and could soon put pressure on Canada to make concessions of its own, namely slashing the exorbitant tariff walls that Ottawa uses to keep foreign milk and cheese at bay.

Mr. Harper and New Zealand Prime Minister John Key are expected to talk about issues ranging from global security threats from Islamic militants in Iraq to Russian aggression in Ukraine. They are talking ahead of a Group of 20 meeting of major economies that both will attend in Australia starting on Nov. 15.

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The conversation is expected to get more awkward when the subject turns to the Trans-Pacific talks, where New Zealand is pushing for Canada to open its dairy markets. The 12 countries in the negotiations, including the United States, announced Monday that significant progress in recent months "sets the stage to bring these landmark … talks to conclusion."

Tiny New Zealand has thrived on rising dairy exports and wants new markets.

It's probably the one file where long-time allies will find themselves at odds in the months ahead, as U.S. President Barack Obama tries to cobble together a deal to liberalize trade among the dozen countries with a combined population of 792 million.

New Zealand and Canada have a lot in common as former British colonies with Westminster-style political systems, big farming interests and significant immigration populations. They are both members of the "Five Eyes" intelligence-sharing alliance of English-speaking countries.

And then there's milk.

"We're the world's biggest dairy exporter, and Canada is probably the most protectionist dairy country in the world," Simon Tucker, New Zealand's high commissioner, said.

"It really is quite an obvious anomaly in the relationship."

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New Zealand has long hoped Canada would change its ways, even insisting in 2011 Ottawa could not join the Trans-Pacific Partnership talks unless it put its "supply management" protections on the table.

Anticipation is rising in Wellington that the trade talks could lower the protectionist walls around Canadian dairy and poultry goods.

Mr. Tucker said Trans-Pacifc talks will only succeed if they manage to achieve real reductions in trade barriers and if this happens, it's hard to imagine negotiating countries would leave the tariff walls protecting Canada's dairy system unaffected.

Tariffs slapped on foreign dairy products can run as high as 300 per cent.

The Canadian government has long insisted it will not make concessions on Canada's "supply management system."

Trade experts say significant obstacles to a Trans-Pacific deal remain, including the question of whether Japan, which is deeply protectionist on some fronts, will agree to major concessions.

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But Mr. Tucker says he thinks Mr. Obama is trying to wrap up TPP talks by the middle of 2015 and that the White House will push hard for an ambitious deal because the Republican-dominated Congress will only approve one that significantly slashes trade barriers.

He said that, while it's up to Ottawa to decide how to structure its dairy industry, the Trans-Pacific Partnership talks could transform the supply-managed sector.

"I've been out talking to dairy farmers and you do find a lot of them privately will talk that they recognize that change is necessary and inevitable," Mr. Tucker said.