While President Obama’s grant of amnesty for nearly 5 million illegal immigrants is drawing furious criticism, a little-known visa program for wealthy foreign investors also is mushrooming on his watch despite a history of fraud and concerns in Congress about potential national security risks.

Since Mr. Obama took office, the number of immigrants entering the U.S. legally under the “EB-5” program has risen nearly 700 percent, from 628 in fiscal year 2008 to 5,115 in fiscal 2014. The number of foreign citizens applying for the visas has grown even faster, from 853 in 2008 to 12,453 in 2014.

“There’s been a major promotion,” said Louis Crocetti Jr., an immigration consultant who formerly led the fraud detection unit at U.S. Citizenship and Immigration Services. “Obviously, it’s very popular. It’s one that’s riddled with all sorts of problems. The agency keeps trying to correct them, but I do believe there’s just an increasing demand and increasing education of the investment opportunities.”

High-profile incidents of EB-5 fraud, and skepticism about the government’s claims of

job creation, have led three Republican senators — Chuck Grassley of Iowa, Bob Corker of Tennessee and Tom Coburn of Oklahoma — to request a federal audit so Congress can evaluate the program before it comes up for reauthorization next year.

Mr. Grassley said whistleblowers have raised serious concerns with national security implications, and he wants to “sort through the vulnerabilities” of the program.

The Government Accountability Office said this month that it has begun the audit, which is expected to be completed by next summer.

To obtain an EB-5 visa, a foreign citizen must agree to spend at least $500,000 on a project that will create at least 10 jobs in the U.S. Investments usually are pooled through “regional centers,” which also have grown exponentially, from fewer than 50 in 2008 to 600 this year.

More than 70 percent of the foreign investors are from China; in return for their investment, they and their family members gain access to permanent residence visas, also known as green cards. The program has become so popular that USCIS temporarily stopped approving applications from China last August because the quota had been reached for the first time.

Immigration lawyers say the program’s popularity began to increase during the deep economic recession of 2007-2009, because it became a source of cheap money for capital improvement projects at a time when government funding and bank loans were drying up.

Kyle Barella, an immigration lawyer in McLean, Virginia, who works with EB-5 applicants, said the program “really boosts the economy.”

“When these investors come here, they send their children to school, they pay their taxes, they buy houses,” he said.

But Mr. Barella said the president’s recent executive action to grant work permits to millions of illegal immigrants has caused enormous resentment among the foreign investors trying to get into the U.S. legally.

“It’s frustrating, and it sends a bad message about incentive,” Mr. Barella said. “Clients are asking, ‘Why should I spend this money the legal way when I can just come over here on a tourist visa, overstay, and in 10 years maybe I’ll get amnesty?’”

Leon Rodriguez, director of USCIS, told a group of stakeholders in the program this month that the applications for EB-5 visas in fiscal 2014 represent more than $5 billion in potential economic investments.

For example, agents of the heavily indebted Pennsylvania Turnpike Commission are seeking 400 wealthy foreign investors to provide $200 million for a $420 million highway construction project to link the turnpike to I-95 north of Philadelphia.

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