BEIJING—After more than a week of a brutal selloff in Chinese stocks, the country’s central bank on Saturday took a rare easing step, cutting both its benchmark interest rates and the amount of reserves certain banks are required to hold.

In a statement, the People’s Bank of China said both steps were aimed at lowering borrowing costs and “stabilizing growth” in the world’s second-largest economy.

The PBOC cut its one-year benchmark lending rate by a quarter of a percentage point to 4.85% and its one-year deposit rate by the same scale to 2%.