India's death toll from the coronavirus pandemic surpassed 20,000 on Tuesday and case numbers surged as the south Asian nation pushed ahead with relaxations to its almost two-month lockdown amid grim economic forecasts.

The rate of both new COVID-19 infections and deaths are rising at the fastest pace in three months, as officials lift a vast lockdown of India's 1.3 billion people that has left tens of thousands without work and shuttered businesses.

The country reported 467 new deaths on Tuesday, taking the toll to 20,160. It also recorded 22,252 new infections, increasing the total to 719,665. India on Monday overtook Russia as the third most affected country globally, behind the United States and Brazil.

But its death rate per 10,000 people is still a low 0.15, compared with 3.97 in the United States and 6.65 in the United Kingdom, according to a Reuters tally.