Germany and France are introducing a government-backed project to develop European cloud infrastructure in an effort to help local providers compete with U.S. technology giants, which dominate the global cloud market.

Amazon.com Inc. and Microsoft Corp. criticized the initiative announced this week, called Gaia-X, saying the project will restrict data services along national borders.

The reach of Amazon, Microsoft and other U.S. giants worries European politicians and corporate executives. Companies in Germany and France, the continent’s economic powerhouses, and in other European Union countries are concerned about depending on technology providers that must comply with the U.S. Cloud Act, WSJ Pro Cybersecurity reported in October. The 2018 law requires American firms to provide law enforcement with customers’ personal data on request, even when the servers containing the information are abroad.

“There’s no answer to the question of how secure our data really is,” Frank Melzer, chief technology officer of Festo AG, a German company that makes robots and other industrial products, said this week at a German digital conference where Gaia-X was announced.

Cloud providers taking part in Gaia-X will be required to certify to their corporate customers that their information remains secure and provide guarantees about where it is stored and how it is processed. Participating in the project would require cloud providers to use the same standards, letting businesses easily move their data from one provider to another.

French and German government officials are set to meet this month with companies interested in participating and the plan is to create a governance structure for the initiative before the end of the year, the German Economy Ministry said. A spokeswoman declined to elaborate.

Some European companies that use large American cloud providers say those services are more competitively priced than cloud services in Europe, WSJ Pro previously reported. Gaia-X could lower transaction costs by standardizing contracts and processes between cloud providers and customers, the German Economy Ministry said. It didn’t provide details about how much governments plan to invest in the project.

Gaia-X is an “important initiative” but details about performance, services and cost will determine whether European cloud providers can compete with non-European suppliers, a spokeswoman for German bank Commerzbank SA told WSJ Pro Cybersecurity in an email. Commerzbank uses cloud services from Alphabet Inc.’s Google and International Business Machines Corp. , she said.

Another goal of the infrastructure plan is to help European companies in industries such as manufacturing and health care in their efforts to develop algorithms and artificial intelligence without relying on foreign technology providers, government officials said.

“We need something like an Airbus for artificial intelligence,” German Economy Minister Peter Altmaier said at this week’s conference.

Roberto Viola, a European Commission official focused on communication and technology, also compared Gaia-X to Airbus SE, the European multinational plane maker that is the main competitor to U.S.-based Boeing Co.

“Europe remains open to the world, but with an ambition…to have digital sovereignty,” he said, speaking at the same conference.

Microsoft and Amazon said they are able to host corporate data securely and criticized the German and French governments’ approach.

A Microsoft spokesperson said digital sovereignty is a legitimate goal, adding, “in the cloud age, however, we think it is wrong to define sovereignty solely along territorial borders.” Instead, sovereignty needs “the most powerful cloud solution.”

Microsoft is interested in participating in Gaia-X, the spokesperson said.

The German Economy Ministry said non-EU companies will be able to take part in the initiative if they “share our goals of data sovereignty and data availability.” A ministry spokeswoman declined to comment on whether U.S.-based companies can meet those goals if they comply with the U.S. Cloud Act.

A spokesperson for Amazon’s cloud provider Amazon Web Services said that Germany and France’s plan “removes many of the fundamental benefits of cloud computing for customers—it restricts freedom of choice, flexibility, and ability to scale globally, without increasing security.”

Write to Catherine Stupp at Catherine.Stupp@wsj.com