Stocks tumble further on Tuesday, dragging the benchmark Shanghai index to its lowest level since last December, amid global stock market panic.

The benchmark Shanghai Composite Index opened at 3,004.13 points, down 6.41 percent. The Shenzhen Component Index opened 6.91 percent lower at 10,212.47.

The ChiNext Index, tracking China's NASDAQ-style board of growth enterprises, opened 7.27 percent lower at 1,996.04 points.

The gauge plunged after sinking 12 percent last week, despite the State Council granting pension funds access to equities for the first time over the weekend.

These funds will be able to invest up to 30 percent of their net assets or 600 billion yuan in total ($97 billion) in the country's stocks, equity funds and balanced funds, according to rules published by the Cabinet.