While businesses often chafe at new federal regulation, executives at companies like Microsoft, Google, OpenAI and Meta have all said that they fully expect the United States to regulate the technology — and some executives, surprisingly, have seemed a bit relieved. Companies say they are worried about corporate liability if the more powerful systems they use are abused. And they are hoping that putting a government imprimatur on some of their A.I.-based products may alleviate concerns among consumers.

The chief executives of Microsoft, Google, OpenAI and another A.I. start-up, Anthropic, met with Ms. Harris in May, and in July they and three other companies voluntarily committed to safety and security testing of their systems.

“We like the focus on innovation, the steps the U.S. government is taking to build an A.I. work force and the capability for smaller businesses to get the compute power they need to develop their own models,” Robert L. Strayer, an executive vice president at the Information Technology Industry Council, a trade group that represents large technology companies, said on Monday.

At the same time, several companies have warned against mandates for federal agencies to step up policing anticompetitive conduct and consumer harms. The U.S. Chamber of Commerce raised concerns on Monday about new directives on consumer protection, saying that the Federal Trade Commission and the Consumer Financial Protection Bureau “should not view this as a license to do as they please.”

The executive order’s security mandates on companies were created by invoking a Korean War-era law, the Defense Production Act, which the federal government uses in what Mr. Biden called “the most urgent moments.” The order requires that companies deploying the most advanced A.I. tools test their systems to ensure they cannot be used to produce biological or nuclear weapons. The companies must report their findings from those tests to the federal government — though the findings do not have to be made public.