Some U.S. immigration service employees are accusing the agency's director of fast-tracking approvals earlier this year of a foreign-investor-funded project to rebuild the landmark Sahara casino and hotel in Las Vegas, over the objections of internal agency analysts who were suspicious about the source of the funds.

In internal emails sent to Sen. Chuck Grassley by agency workers, Alejandro Mayorkas, director of U.S. Citizenship and Immigration Services and the nominee for the No. 2 post at the Department of Homeland Security,...