The federal government’s E-Verify program that seeks to reduce the hiring of illegal immigrants is becoming increasingly popular, with 1,000 new businesses signing up each week despite concerns about its reliability.

More than 124,000 businesses are signed up for the Web-based identification program that enables employers to check whether an employee is authorized to work, according to U.S. Citizenship and Immigration Services. Employers enrolled include restaurants, hospitals and temporary employment agencies.

The Obama administration announced this month it wanted Congress to allocate $12 million more to the program in the next fiscal year, bringing the program budget to $112 million. And Department of Homeland Security Secretary Janet Napolitano said in a congressional hearing the program is “a cornerstone of workplace enforcement across the country.”

“E-Verify is an essential tool for employers to maintain a legal workforce,” she said in written testimony. “Nevertheless, room for improvement always remains.”

Napolitano said the government plans to improve accuracy of the databases and to strengthen the training of employers to protect workers against discrimination.

E-Verify, run by the Department of Homeland Security, uses government databases to check the names, dates of birth and Social Security numbers of new hires to determine whether those people are eligible to work in the U.S. The program is voluntary, though a few states have passed laws requiring all businesses to participate, and several others mandate its use by public employers.

At the end of June, all federal contractors and subcontractors will be required to use the program. Last fiscal year, more than 6.6 million names were checked under the program, according to the citizenship agency.

E-Verify is an effective way to attack the jobs magnet for illegal immigrants, said Roy Beck, executive director of Numbers USA, which favors stricter controls on immigration.

Beck said he hopes the funding increase will result in more employers signing up.

“If there aren’t jobs, they stop coming,” he said. “We would rather solve the immigration problems not with people wearing uniforms and guns but simply with papers, just running someone through the computer.”

But Angela Kelley, vice president for immigration policy at the Center for American Progress think tank, said E-Verify is not “ready for prime time.”

“Supporters frame this as an immigration enforcement solution,” she said. “It’s really American workers having to ask the government for permission to work.”

Immigration attorney Peter Schey said though the program might be politically popular, it is unlikely to solve the issue of illegal immigration and will only push more undocumented workers underground.

“They won’t leave the country because of E-Verify,” he said.

Business groups generally support E-Verify but criticize the error rate. The government reports that the program has a 96 percent accuracy rate. But even a small error rate could disqualify millions of workers if the program were to be expanded to the entire workforce, said Randel Johnson, vice president of labor, immigration and employee benefits for the U.S. Chamber of Commerce.

Despite that, many businesses want to be on the right side of the law and are willing to try out the system if it helps protect them from inadvertently hiring undocumented workers, said Tamar Jacoby, president of ImmigrationWorks USA, a national federation of employers.

But Jacoby said there is an even bigger problem for employers.

“We can’t have a workable system of E-Verify if we don’t have a legal immigrant workforce,” she said.

That’s why many agricultural companies haven’t signed on, said Bryan Little, director for labor affairs for the California Farm Bureau. Little said he worries about having enough people to work the fields.

“It’s not in our benefit to hire illegal workers,” he said. “The way the marketplace looks right now, farmers don’t have a better option available to them.”