An attendee wears a Galaxy Gear Virtual-Reality headset during the TechCrunch Disrupt SF 2015 conference in San Francisco, California in September.

BOSTON – President Donald Trump wants to overhaul a visa program that allows U.S. companies to hire foreign workers, a move that could affect hundreds of Massachusetts companies from high-tech businesses to hospitals and colleges. 

On Tuesday, Trump signed an executive order directing the State Department and other agencies to review the H-1B visa program. He said it undercuts American workers by importing legions of foreign workers who make less pay, driving down wages.

“Right now H-1B visas are awarded in a totally random lottery, and that’s wrong,” Trump told workers at a tool manufacturing company in Wisconsin. “They should be given to the most skilled and highest paid applicants, and they should never, ever be used to replace Americans.”

The tech industry argues that the program is vital, especially since it encourages students to stay in the U.S. after getting degrees in high-tech specialties.

There aren’t enough skilled American workers for all of the high-tech jobs employers are seeking to fill, according to the industry advocates.

“Any policy that hinders our ability to attract the best talent would be a major concern,” said Chris Anderson, president of the Massachusetts High Technology Council. “Nationwide we are one of the leading technology states.”

Anderson said there are “opportunities” to improve the visa program, specifically by lifting the federal government’s cap on H-1B visas, currently set at 85,000 per year. 

“But if we move the other way, by reducing the number of visas, we would be damaging a very important part of the talent pipeline for the technology community,” he said.

The tech sector for decades has lobbied to increase the number of H-1B visas.

“Immigrants play a huge role in the American economy, especially in the tech sector,” said Matt Mincieli, Northeast region executive director for TechNet, which advocates for technology companies. “We want to see this program expanded, not scaled back.”

To obtain a visa, an employer must offer a job to a foreign worker, then apply for his or her visa. Workers with at least a bachelor’s degree can be brought into the country for up to three years, with the possibility of extending the stay to six years.

Employers are required to pay the prevailing wage for the job, which depends on skill level, the job description and its location. Companies paying H-1B workers less than $60,000 per year are required to show that they couldn’t hire Americans for the same jobs.

But critics of the visas, including Trump, argue that some companies abuse the system and use it to cut costs by hiring cheap labor.

In 2013, Infosys Ltd., India’s second-largest software exporter, agreed to pay $34 million to the United States in an immigration case to settle claims that it had abused the visa program.

Federal prosecutors allege the company circumvented the requirements of the H-1B visa program by using a different category of visas, which only allow for temporary entrance to the U.S. for limited business purposes.

The company denied any wrongdoing under the settlement.

In February, the Trump administration said it would temporarily halt expedited applications for H-1B visas as part of a broader crackdown on immigration.

Nationwide, demand for H-1B visas has outstripped supply.

In recent years, the government has held a computer lottery to award the non-immigrant visas. Congress caps the number of visas annually at 65,000, with an additional 20,000 set aside for workers who have master’s degrees or higher.

The tech industry says the total number of visas issued through the program is likely much higher than the annual cap suggests, because of extensions and job transfers.

Figures of how many visas are issued by state weren’t available, but last year the government cleared at least 41,182 foreign workers to be hired by Massachusetts companies, according to the U.S. Labor Department.

Massachusetts ranks sixth in the nation in the number of H-1B workers — behind California, New Jersey, Texas, New York and Florida, according to the U.S. Citizenship and Immigration Services.

Among the state’s top employers of H-1B workers are Harvard University, State Street Bank, Brigham and Women’s Hospital, IBM and Deloitte Consulting.

Most employers in the state hiring foreign workers are filling jobs for programmers, software engineers, consultants and analysts, according to the Labor Department.

Martha Farmer, CEO of North Shore Innoventures, a business incubator for life sciences and bio-tech companies at Beverly’s Cummings Center, said educated foreign workers increase innovation at U.S. technology firms and contribute to local economies.

“Nearly half of the companies in our incubator were started by people who weren’t born in the United States,” she said. “People who are willing to move to another country to start a company are entrepreneurial by definition.”

She said limits on non-immigrant visas such as the H-1B program make it harder for many foreign students who are educated in Massachusetts to find work in the state after graduation.

“They’re highly qualified and want to stay,” she said. “We’re losing an opportunity.”

Congress for years has debated proposals to reform the visa program.

Rep. Darrell Issa, R-California, introduced a bill aimed at punishing outsourcing companies. Under his plan, companies paying H-1B workers less than $100,000 will have to show they couldn’t hire Americans for the same jobs.

Another proposal, by Sens. Dick Durbin, D-Illinois, and Charles Grassley, R-Iowa, would require companies seeking H-1B visas to first make a “good-faith effort” to hire Americans.

“Hopefully whatever changes come out of this discussion will strengthen the program,” Mincieli said. “Because it’s vital to the tech industry and the nation’s economy.”

Christian M. Wade covers the Massachusetts Statehouse for North of Boston Media Group’s newspapers and websites. Email him at cwade@cnhi.com.