FRANKFURT — A free-trade agreement between the United States and Europe, elusive for more than a decade but with a potentially huge economic effect, is gaining momentum and may finally be attainable, business and political leaders say.

Arduous negotiations still lie ahead, but if technical hurdles can be overcome, supporters of a pact argue, it could rival the North American Free Trade Agreement in scale and be a cheap way to encourage growth between the European Union and the United States, which are already each other’s biggest overseas trading partners.