Minor traffic offenses, including driving without a license, will not be counted at all against applicants. Driving offenses are an important point because all but three states — New Mexico, Utah and Washington — deny licenses to illegal immigrants.

Applicants, who must attend an appointment and submit to background checks, might have to wait several months for a ruling. The wait will depend on the backlog.

The agency said the number of applications will determine how many employees it hires, and it did not provide an estimate for the total cost of the program. The Associated Press reported last month that Homeland Security Department internal documents estimated hundreds of employees may be hired and that the total cost could top $585 million.

The internal documents estimated that the number of applicants might top 1 million in the first year, or more than 3,000 a day. It will cost between $467 million and $585 million to process applications in the first two years, with revenues from fees paid by immigrants estimated at $484 million.