Because the firms have relatively light physical presences in Europe, they benefit from the current system, which taxes companies based on where their operations and assets are — and not where their sales are generated. The European Union has said this has allowed tech companies to pay less than half the effective tax rate of other multinationals, and European leaders want to tax them in a way that takes into account where their users are.

Mr. Mnuchin has spent much of his time discussing the issue at international forums with finance ministers from around the world.

During meetings of the International Monetary Fund and the World Bank in April, Mr. Mnuchin said it was a “priority” to find an international solution, and he pressed France and Britain to abandon their own tax plans once a compromise is reached.

At the Group of 20 finance ministers meeting in Japan in June, Mr. Mnuchin underscored his concerns, and the finance ministers agreed in their communiqué to work toward finding a common set of rules to close loopholes that global technology companies have been using to reduce their tax bills.

“I’m not in favor of the current digital tax that has been proposed by France and the U.K.,” Mr. Mnuchin said, warning a system of unilateral digital taxes would not work. “We have significant concerns with both of those.”

The United States has called for a tax that is based on companies’ income, not sales, and said specific industries should not be singled out with a different standard. The Treasury secretary has dispatched his deputy, Justin Muzinich, to help broker an agreement. The Organization for Economic Cooperation and Development released a “road map” in May, agreed to by nearly 130 countries, toward finding agreement on a global digital tax plan.

France has said that it will repeal its tax once a group agreement is reached. The subject will come up again when finance minsters gather in Chantilly, France, for the summit of the Group of 7 industrialized nations next week. Bruno Le Maire, the French finance minister, has suggested that France’s tax will help accelerate an international pact.