HONG KONG — China’s central bank on Tuesday cut its benchmark interest rate and freed banks to lend more, the latest signs of the government’s growing distress over slumping stocks and slowing economic growth.

The central bank’s action followed a global stock market rout in which China led the declines. The main Shanghai share index plunged another 7.6 percent on Tuesday, to its lowest level this year. That brought its three-day decline to 22 percent, signaling that two months’ worth of attempts by the government to prop up stock prices had limited effects.

On Tuesday, China’s prime minister, Li Keqiang, acknowledged that the country was feeling the effects of market turbulence, but insisted that the economy remained sound.

“Currently, global economic trends are opaque and confusing, and market volatility is quite large, and this has had some impact on the Chinese economy,” Mr. Li said, according to a report on Chinese television news. “But fundamentally the overall stability of the Chinese economy has not changed, and positive factors sustaining a turn for the better in the real economy are accumulating.”

China, he added, would be able to fulfill its economic goals for the year. Mr. Li also noted that there would be no continued depreciation of the renminbi currency after a sharp devaluation earlier this month. The currency “can maintain fundamental stability at a reasonable and balanced level,” he said.

Even so, the tumult has prompted further action by the leadership.

In an aggressive two-part move on Tuesday, the central bank lowered the benchmark lending and deposit rates by 0.25 of a percentage point. It also cut the so-called reserve requirement ratio for the amount of cash that banks are required to hold in reserve by 0.5 of a percentage point.

It was China’s fifth interest rate cut since November, and the fourth reduction of the reserve ratio since February. The central bank made a similar tandem cut to both rates in June, when the stock market first began to fall from its peak, but that reduction of the reserve ratio did not apply to the biggest banks.

Cutting interest rates may help lift the economy, as signs have proliferated in recent weeks that growth is slowing faster than some official data suggest. A survey released on Friday showed that output in China’s manufacturing industry had contracted in the first three weeks of August at the fastest pace since the depths of the financial crisis.

“Currently, there are persisting downward pressures on the country’s economic growth,” the central bank, the People’s Bank of China, said in an explanation that accompanied the announcement Tuesday evening. “There has also been quite large volatility in global capital markets recently, and monetary policy tools need to be applied more flexibly.”

The central bank also made a step toward interest rate liberalization by removing the upper limit on interest rates for fixed-term deposits of more than one year. With inflation in China generally low, the bank said the time was ripe for such steps. “This marks another important step forward in interest rate marketization reforms for our country,” it said.

While the moves may bolster markets, the central bank most likely had another focus in cutting the reserve ratio. Like many emerging economies across the world, China in recent months has been fighting capital outflows, which rose to a record $70 billion in July. And they probably increased this month after China’s surprise devaluation of the renminbi. Investors are moving their money out of the country because they are worried that the currency could fall further, and they are seeking better returns elsewhere.

At the same time, China has been struggling with deflation, or falling prices, in its industrial sector for more than three years. Injecting more funds by freeing banks to lend more should help soften the blow of deflation and stem capital outflows.

Li-Gang Liu, the chief China economist at the Australia and New Zealand Banking Group, estimated the reserve ratio cut would immediately insert around 650 billion renminbi, or around $100 billion, into the banking system.

The cut “will spur bank lending and lower firms’ funding costs,” he wrote in a research note on Tuesday after the central bank’s announcement. But Mr. Liu doubted these latest measures alone would be enough to meet the government’s economic growth target of about 7 percent this year. He continued: “Further monetary policy easing by the People’s Bank of China is still in the cards.”

By August 25, 2015 in The New York Times