"The existing interpretation was so broad as to be unworkable," Leahy, D-Vt., said in a statement. He said the previous rule barred applicants for reasons "that no rational person would consider."
Republican lawmakers argued that the administration is relaxing rules designed by Congress to protect the country from terrorists.
Rep. Bob Goodlatte, chairman of the House Judiciary Committee, called the change naive given today's global terrorist threats.
"President Obama should be protecting U.S. citizens rather than taking a chance on those who are aiding and abetting terrorist activity and putting Americans at greater risk," said Goodlatte, R-Va.