HONG KONG — China finally admitted it has a growth problem — and that is a big step to getting the global economy back on track.

For months, Beijing avoided broad stimulus measures, signaling that it was comfortable with the country’s slowing growth. But China’s pockets of weakness, coupled with the continuing woes in Japan and Europe, prompted anxiety in the financial markets.

Now China is changing its stimulus stance, announcing a surprise interest rate cut on Friday. The action will lift the country’s flagging housing market and large state-owned companies, as well as bolster other nations that have come to rely on those core parts of China’s economy.

In cutting rates, China joins the parade of global policy makers who are stepping up their stimulus efforts to support growth. They are filling a void left by the United States Federal Reserve, which just ended a six-year bond-buying campaign that has kept borrowing costs low and has encouraged spending worldwide.