Amid a significant surge in Covid-19 cases in six states, India’s health ministry has advised local governments to take a risk assessment-based approach to prevent and contain the infection from spreading further, officials said Friday.

The federal health ministry wrote a letter on Thursday evening to the states of Maharashtra, Karnataka, Gujarat, Kerala, Tamil Nadu, and Telangana, asking them to pay attention to testing, treating, tracking, and vaccination.

A few states are reporting...