The study "America's New Immigrant Entrepreneurs: Then and Now," shows that 24.3 percent of engineering and technology start-up companies have at least one immigrant founder serving in a key role. Indian-born entrepreneurs, representing 33 percent of the companies, dominated the group.

The study paid particular attention to Silicon Valley, where it analyzed 335 engineering and technology start-ups. It found 43.9 percent were founded by at least one immigrant.

"High-skilled immigrants will remain a critical asset for maintaining U.S. competitiveness in the global economy," wrote the authors of the study, sponsored by the Kauffman Foundation, a non-profit organization that promotes entrepreneurship.

One of the authors, Singularity University's Vivek Wadhwa, called for a visa designed for entrepreneurs.

"If we had a startup visa, we would have tens of thousands of new startups nationwide," he said via email.

In recent years, the number of start-ups overall in Silicon Valley has mushroomed, as entrepreneurs have found it easier to access "seed" or early capital.

Those opposed to relaxing immigration rules, including many unions, argue that immigrants displace higher-paid U.S. workers in key technology professions such as software engineering.

And while many lawmakers support allowing more immigrant entrepreneurs into the country, powerful Washington lobbies do not want to relax rules for one group without addressing the broader issue of illegal immigration.

Immigration is a flashpoint among Hispanic voters, a key voting block that both President Barack Obama and his Republican rival Mitt Romney are courting.

President Obama recently told TV network Univision he considers the lack of comprehensive immigration reform his "biggest failure" during his first term in office.

Romney has promised to put in place an immigration reform system and has said he believes the Republican party is the "rightful home" of Hispanic voters.

Some 40 million people living in the U.S., or 13 percent of the population, were born overseas, according to the U.S. Census Bureau.