The search for a new agreement on how countries should tax multinational corporations advanced Wednesday, as international negotiators proposed rules that would force tech giants such as Facebook Inc., Amazon.com Inc. and Alphabet Inc.’s Google to pay more tax in countries where customers consume their products and services.

Tensions between the U.S. and other governments have risen following the introduction or announcement of a series of special taxes on digital services that mostly fall on large U.S. technology companies....