A dairy farmer walks with his cow during during a protest against the Trans-Pacific Partnership (TPP) trade agreement in front of Parliament Hill in Ottawa, Canada September 29, 2015. REUTERS/Chris Wattie

OTTAWA (Reuters) - Unhappy Canadian dairy farmers parked dozens of tractors in central Ottawa and walked their cows down the main street opposite Parliament on Tuesday to protest trade talks they said could cripple them.

Canada is one of 12 Pacific Rim countries trying to nail down a trade deal in Atlanta this week. The United States, New Zealand and Australia want Canada to start dismantling a system of tariffs that keep domestic prices high and imports expensive.

Farmers said they would be flooded by cheap foreign milk if the so-called supply management system were to end. The issue could cost the ruling Conservatives crucial rural votes in what looks set to be a hotly contested election on Oct 19.

“If they bring in so much milk from the States our Canadian market will be flooded pretty easily ... it’s stressful to think that the government will sell us out to the Americans,” said Chris Ryan as he struggled to control his cow Ninja.

“I’m usually a Conservative voter but this year I don’t think I’ll be going for them,” said Ryan, who comes from St. Isidore to the east of Ottawa. The area is currently represented by the Conservatives.

Prime Minister Stephen Harper, who has said Canada must sign onto the proposed Trans-Pacific Partnership (TPP) free trade pact, said on Tuesday that Ottawa would defend supply management but gave no details of what concessions Canada might make.

The Trans-Pacific Partnership seeks to cut trade barriers and set common standards for 40 percent of the world economy and will be a legacy-defining achievement for U.S. President Barack Obama.

“They don’t see how it affects the farmers, they just see the big picture,” said farmer Travis McFadden from Navan to the east of Ottawa, which is also represented by a Conservative legislator.

This week the federal farm, fisheries and natural resources ministers released statements from industry groups saying it was crucial for Canada to be part of TPP.