PRESIDENT REAGAN was absolutely right to end the Justice Department's misguided investigation into transatlantic airline fares. For a decade, under three presidents, the Justice Department has been carrying on a persistent campaign to extend the jurisdiction of American antitrust law to foreign countries. The foreign countries are right in seeing these attempts as infringements of their sovereignty. The result has been a series of angry collisions with this country's closest allies, beginning with Canada and Britain.

It began nearly a decade ago with the uranium cases. The Canadian government, among others, had set a minimum price for uranium, and the Justice Department set up a grand jury to look into it. The Canadians replied, hotly, that they felt no obligation to conform Canadian energy policy to the Justice Department's antitrust theories. They were tactful enough not to observe that the American government has frequently and routinely set minimum prices for a vast range of commodities from oil to corn. If collusion among governments to raise prices were a crime, why didn't the Justice Department have a grand jury investigate OPEC? But Justice was never foolish enough to try that.

The department has gotten into trouble when it has tried to apply American law to foreign governments' policies, as in the uranium cases, or to foreign governments' operations, as in the airline tickets. British Airways is owned by the British government. The Justice Department has been trying to argue that anybody engaged in business that touches the United States must be bound by American rules, even in their own countries. You hardly need to be told that Britain takes a different view. Price discussions among competing airlines are both legal and traditional in London, and the British government does not intend to pay damages in an American court for following its own law.

But if Mr. Reagan has properly told Justice to call off its grand jury regarding the airline fares, he has yet to apply the same principle to the other departments of his government. The Commerce Department tried to enforce American export restrictions on the Europeans two years ago in its effort to force them to drop the Siberian gas pipeline deal with the Soviets. Those efforts failed, predictably, producing little more than severe irritations among the Western allies. Currently the Pentagon is trying to get an extreme version of extraterritorial reach written into the Export Administration Act; this time it's Commerce that is rightly resisting.

Mr. Reagan isn't running the Roman Empire. There is only one way to make international rules that stick, whether on exports to the Soviets or cut-rate airline tickets. That's through voluntary negotiation. It's the hardest way to do it, but the only way that produces useful results.