FORTUNE — Readers of the Washington Post may run across a full-page ad this week that implores them to “Deny NAI.”

That somewhat cryptic message is part of a seven-figure ad campaign by the Air Line Pilots Association, International — the group’s latest attempt to keep Norwegian Air Shuttle, Europe’s third-largest budget carrier, from bringing its low-cost model to the United States as Norwegian Air International.

Norwegian says the “misleading” and “dishonest” campaign simply shows that American airlines and pilots are afraid of competition. But industry groups here say they’re up for more competition, so long as it doesn’t come in the form Norwegian Air wants to take: a Norwegian-named airline based in Ireland that employs Thailand-based crews through a Singaporean pilot supply company.

“We’re fine with competition as long as it’s on a level playing field,” Michael Robbins, the Pilots Association’s director of government affairs, told Fortune.

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The discount airline currently operates a long-haul business and even flies between Oslo and New York’s Kennedy Airport under a temporary permit issued by the government in Norway. To offer additional flights between Europe and the U.S., Norwegian filed a still-pending application for a permanent permit with the U.S. Department of Transportation in December.

Robbins says the Pilots Association rarely opposes permit applications, but it took issue with Norwegian’s filing because the airline decided to move its long-haul business from Oslo to Dublin, Ireland earlier this year. It filed its permit application with the Department of Transportation as a “foreign air carrier of Ireland” even though it offers no flights to or from the country.

The Pilots Association has painted the move as part of a scheme by Norwegian Air to evade Norway’s strict labor laws and its collective bargaining requirements. Ireland has weaker labor laws that will allow the airline to keep labor costs low by outsourcing its crew to Asia — a strategy that ran aground of Norway’s stricter regulations.

“At bottom, [Norwegian] seek[s] to establish a new flag of convenience in Ireland to avoid Norway’s labor laws and lower labor costs,” Delta Air Lines DAL , United Airlines UAL , and American Airlines AAL said in a joint letter to the Transportation Department.

“That’s why we’re calling it Walmarting,” says Edward Wytkind, president of the Transportation Trades Department of the AFL-CIO, which represents airline industry unions. “This could dumb down labor standards to the point where it’s hard to make a living wage in the airline industry.”

Norwegian, meanwhile, says it moved its long-haul business to access future air traffic rights between the EU (Norway is not a member) and Asia, Africa, and South America. Another reason: Ireland plans to fully adopt the 2001 Cape Town Treaty, which created international standards for transactions involving movable property like airplanes.

But the Pilots Association argues that the airline is labor law venue shopping, which is prohibited by the U.S.-EU Air Transport Agreement that Norwegian cited when filing its permit application. The 2007 agreement gives airlines in the U.S. and EU member states, and some additional country signatories — including Norway — the right to freely fly across each other’s borders. Norwegian “wants to operate outside the rules of the agreement at the same time they try to use the benefits afforded by the agreement,” Wytkind says.

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The big bucks the Pilots Association plans to spend on its campaign against Norwegian illustrates just how much is at stake for the American airline industry. The approval of Norwegian’s air carrier permit would “set a new precedent for flag of convenience schemes to be set up elsewhere in Europe,” Robbins says. “Other airlines could move out of countries with strict labor laws to countries with lax laws, and that’s explicitly what we wanted to prevent with the U.S.-EU Agreement.”

The Pilots Association has drawn a parallel between the risk Norwegian poses and what’s happened to the U.S. maritime industry, which allows a vessel to be registered in a country different from its ownership and operate under the laws of the country of registry. “The practice precipitated the decline of the industry and the loss of tens of thousands of U.S. maritime jobs, as companies flew the flag of countries with the weakest labor and tax laws and regulations,” the association said in a statement.

A Norwegian spokesman, meanwhile, insists that the backlash it faces is all about the competition and industry upheaval it represents: “It’s obvious that they don’t want the American public to get access to inexpensive airfares to Europe.”