BEIJING (Reuters) - China's annual consumer inflation slowed to 2.1 percent in May from April's 2.4 percent, data showed on Sunday, below market expectations and adding to views that the world's second largest economy could slow further in the current quarter.

The National Bureau of Statistics also said that China's producer prices fell 2.9 percent last month from a year earlier, compared with a drop of 2.6 percent in April.

Economists polled by Reuters had expected annual consumer inflation of 2.5 percent and factory-gate prices to fall 2.5 percent in May.

"The inflation data showed China's economic growth continued to slow down. Q2 growth is probably even slower than Q1. In particular, the PPI data showed very weak demand," said Jianguang Shen, chief China economist at Mizuho Securities Asia in Hong Kong.

The subdued inflation will enable China to keep an easy monetary stance and some see the possibility that the People's Bank of China could cut rates later this year to reduce financing costs for struggling Chinese firms, provided that housing inflation does not flare up.

"China has rising room and the possibility to cut interest rates in the second half of this year," Shen added.

"The financing cost for companies is very high now and the central bank should further pursue interest rate liberalization. China's fiscal policy in the second half needs to protect consumption growth and support investment."

China's economy grew at its slowest pace for 13 years in 2012, and it has so far surprised on the downside, bringing warnings from some economists that the country would even miss its annual growth target of 7.5 percent.

On Saturday, data showed that China's exports posted their lowest growth rate in almost a year in May while imports unexpectedly fell, underlining concerns that growth in the world's second-largest economy could slow anew in the second quarter.

Government economists from top think-tanks in Beijing told Reuters this week that the new leadership of President Xi Jinping and Premier Li Keqiang will tolerate quarterly growth to slip as far as 7 percent before hitting the stimulus button.

Li had struck a more upbeat note on Saturday, being quoted by state television as saying that China's economy was generally stable, growth was within a "relatively high and reasonable range" and the employment situation was stable.

Month-on-month, consumer prices fell 0.6 percent in May versus a forecast for a drop of 0.2 percent.

Over 80 percent of the monthly fall in the CPI was accounted for by a fall in vegetable prices as supply increased due to warm weather. Vegetable prices fell 13.8 percent in May from April, dragging down the month-on-month headline CPI by 0.5 percentage points.

(Reporting by Langi Chiang and Jonathan Standing; Editing by Ron Popeski)