Dozens of countries are stepping up efforts to levy new taxes on technology giants such as Alphabet Inc. and Facebook Inc., hoping to capture revenue from digital services as economic activity increasingly shifts online.

Inspired by European Union proposals to impose a tax based on the revenue of tech companies rather than their profit, South Korea, India and at least seven other Asian-Pacific countries are exploring new taxes. Mexico, Chile and other Latin American countries too are contemplating new taxes aimed at boosting...