Talks to remake the North American Free Trade Agreement are starting off today with an early dispute — over how to settle disputes.

Under Nafta, the U.S., Mexico and Canada have resolved tariff conflicts by submitting them to expert panels that can sustain or overturn tariffs. The system has helped guide the trilateral relationship for 23 years.

Now the U.S. wants to do away with those dispute-resolution panels, while Canada is digging in on its insistence that they are a crucial tool for Canadian firms to use to fight tariffs imposed by its powerful southern neighbor. Mexican senators have also called for retaining the mechanism.

Though the system for resolving tariff disputes is only one of many issues that U.S. officials are expected to put on the table in the talks that begin Wednesday in Washington, it is a particularly divisive one. For President Donald Trump, the panels’ power to overturn tariffs strikes at the heart of his “America First” trade policy and his campaign’s spirited defense of measures to protect U.S. industries against what he sees as unfair trade practices.

“This first session could be quite confrontational,” said Fred Bergsten, founder of the Peterson Institute of International Economics in Washington and a member of the U.S. advisory panel for trade negotiations. He expects the U.S. to put the issue on the negotiating table early in the process.

Without Chapter 19 — the portion of Nafta that creates the panels — disputes over tariffs would end up in national courts or before the World Trade Organization, a body the administration also views with skepticism.

The divide is worrying to business groups that want to ensure the talks stay on course. Major changes to Nafta have to be approved by all three countries’ leadership, plus their legislators. Business lobbyists and former trade officials say gridlock could lead to renewed threats from member countries to pull out of the deal or feed political opposition during election seasons.

The opening bids suggest a compromise won’t be easy.

“Canada absolutely stands very firm in the importance of having such a mechanism,” Foreign Minister Chrystia Freeland said this week as she unveiled the country’s objectives ahead of the Nafta talks.

Similarly, Mexico’s Economy Minister Ildefonso Guajardo said the current system provides a deterrent against the improper use of duties. Dismantling it could end up hurting exporters in all three countries, he told The Wall Street Journal in a recent interview.

A U.S. trade official told reporters Tuesday that Washington plans to “be quite ambitious in this first round.”

One question is whether the early rhetoric will give way to compromise once the give and take of the negotiations begin. Trade negotiations are all about compromise, and Chapter 19 could end up being a bargaining chip in a broader set of concessions each side seeks.

“Everything that’s released publicly is a negotiating position,” said Celeste Drake, a senior expert at the AFL-CIO, the biggest U.S. labor federation. “There is always a middle ground if negotiators are willing to work.”

U.S. labor groups tend to oppose Chapter 19, saying tariffs levied on the grounds of alleged dumping or subsidies can be challenged in the court system or through the WTO. Ms. Drake said the Trump administration should press hard to resolve differences with the other governments to achieve the best deal for workers.

Stephen Powell, a former senior counsel at the Commerce Department who has written extensively on the dispute-resolution process, said given the historical importance Canada places on Chapter 19, it would likely demand a “very large concession” for abandoning the system. “Canada can certainly insist on something very big, so can Mexico,” Mr. Powell said.

But for Mr. Trump and U.S. trade representative Robert Lighthizer, Chapter 19 symbolizes an erosion of sovereignty, since the panels have primarily been used to overturn tariffs imposed by the U.S. Commerce Department on Canadian and Mexican products. The issue is of particular note to Mr. Lighthizer, who spent about three decades as a Washington trade lawyer arguing for the types of tariffs that can be overturned under Chapter 19.

Mr. Lighthizer’s office in July left flexibility in most of its official objectives for Nafta talks, but it said clearly in the trade remedy section that it wanted to “eliminate the Chapter 19 dispute settlement mechanism.”

The third-party dispute system dates back to 1987, when President Ronald Reagan granted Canada’s demands for an independent resolution mechanism to salvage the U.S.-Canada free-trade pact, Nafta’s predecessor. The issue threatened to become a deal breaker 30 years ago, and it took the intervention of Canadian Prime Minister Brian Mulroney and U.S. Treasury Secretary James Baker to get resolved.

Colin Robertson, a Canadian negotiator at those 1987 talks, said Canada’s business community pushed for independent panels after years of amassing large legal bills unsuccessfully fighting U.S. trade sanctions in the American courts.

Since coming into force, nearly 150 Chapter 19 cases have been adjudicated, two-thirds of which were brought by either Canada or Mexico against the Commerce Department.

The rate at which countries are filing Chapter 19 cases has recently slowed, with panels having dealt with just over a dozen cases since 2010. Trade watchers say the falloff in cases stems in part from the greater U.S. focus on trade cases involving China, and illustrates how Nafta has ushered in greater integration across the North American economy, with firms owning assets in each of the three countries. “There’s no us versus them any more,” said Peter Glossop, trade lawyer with Toronto firm Osler Hoskin & Harcourt.

Canada hasn’t always had clear-cut wins in Chapter 19 cases, but some — most notably dealing with the decadeslong spat over lumber — have gone its way. Ottawa’s most recent win was in April, when an independent panel directed the U.S. Commerce Department to roll back the bulk of a proposed 20% tariff on a type of glossy magazine paper made by a mill in the Atlantic coast province of Nova Scotia. The U.S. claimed the mill unfairly benefited from power rates set by the province’s regulator, but the panel found that the U.S. offered little evidence to support its case.

“We certainly knew that with Chapter 19, all of the facts would be addressed by an independent panel…in a more fair manner,” said Marc Dubé, a senior manager at Port Hawkesbury Paper, the mill that faced the 20% duty.

Write to Paul Vieira at paul.vieira@wsj.com, William Mauldin at william.mauldin@wsj.com and Anthony Harrup at anthony.harrup@wsj.com