NEW DELHI—The U.S. raised India’s aviation-safety ranking after more than a year of effectively barring the South Asian nation’s airlines from adding new flights to the U.S. because of concerns about India’s regulatory oversight.

During a visit Wednesday to India’s capital of New Delhi, U.S. Transportation Secretary Anthony Foxx announced that the Federal Aviation Administration has lifted India’s status a notch to Category 1, confident that it has taken sufficient measures to address the FAA concerns that had led to India’s...