CAMBRIDGE — The Obama administration’s top immigration official says his agency is working to attract and keep more foreign-born high-tech entrepreneurs who are seeking to start companies in the United States, a move he hopes will help the nation retain its edge in an increasingly competitive global economy.

Alejandro Mayorkas, director of the US Citizenship and Immigration Service, acknowledged on Wednesday that his agency ‘‘has not been especially nimble’’ in adapting to fast-paced changes in the business landscape.