Although President Obama has put off an immigration overhaul until next year, the federal agency in charge of approving visas is planning ahead for the possibility of giving legal status to millions of illegal immigrants, the agency’s director said Thursday.

“We are under way to prepare for that,” Alejandro Mayorkas, the director of the agency, the United States Citizenship and Immigration Services, said in an interview. Mr. Obama has told immigration officials that a legalization program would be part of legislation the White House would propose, said Mr. Mayorkas, who became director in August. The agency’s goal, he said, is to be ready to expand rapidly to handle the gigantic increase in visa applications it would face if the legislation, known as comprehensive immigration reform, passed Congress.

The citizenship agency faces a difficult balancing act, preparing for a potential workload bigger than any it has faced, based on legislation in early stages of discussion that is fiercely opposed by many lawmakers in Congress. Also, the agency must work to reduce backlogs and delays that have hampered its performance.

There are no official estimates of the number of illegal immigrants who would apply for legal documents. The Pew Hispanic Center and the Center for Immigration Studies, two research groups in Washington, estimate that at least 10.8 million illegal immigrants live in this country. But a large number of those would not be eligible for legal status for many reasons, including past immigration violations.