* April CPI +0.3% y/y vs Mar +0.1%

* April PPI -2.5% y/y vs Mar -2.8%

* Domestic demand is recovering, analysts say

BEIJING, May 11 (Reuters) - China's consumer prices rose for a third straight month in April, while producer prices extended declines, signaling an improvement in domestic demand, as Beijing navigates challenges in its bid to shore up a shaky economy.

The closely watched numbers follow better-than-expected imports data for April, suggesting a flurry of policy support measures over the past several months may be helping consumer confidence.

Consumer prices edged up 0.3% in April from a year earlier, data from the National Bureau of Statistics showed on Saturday, versus a rise of 0.1% in March and a Reuters poll forecast for an increase of 0.2%.

"Strip out food and energy prices, and the consumer inflation data suggests a comeback in demand, especially in services," said Xu Tianchen, senior economist at the Economist Intelligence Unit.

Core inflation, excluding volatile food and fuel prices, grew 0.7% in April, up from 0.6% in March.

Overall the consumer price index (CPI) rose 0.1% from the previous month, beating a forecast fall of 0.1% in the poll and reversing a drop of 1% in March.

Most China watchers say Beijing still has its work cut out, though, and the momentum might prove unsustainable, as official surveys show cooling factory and services activity, while a lengthy housing crisis shows no sign of easing, boosting the case for more policy support.

"Price hikes by utility companies is another potential driver," Xu added.

"The fiscal strains some local governments are facing affect the subsidies they receive, which could be forcing them to pass the extra cost on to households to make ends meet."

Officials are grappling with municipal debt of $13 trillion, and the State Council, or cabinet, has told heavily indebted local governments to delay or halt some state-funded infrastructure projects.

"The prices data suggests that domestic demand is recovering, supply and demand continues to improve and the outlook for domestic demand and price recovery is optimistic," said Zhou Maohua, a macroeconomic researcher at China Everbright Bank.

"However, consumer prices remain low and the industrial manufacturing sector is still under pressure, reflecting insufficient effective demand and that recovery in the sector is still not sufficiently balanced."

The producer price index (PPI) dropped 2.5% in April from a year earlier, easing from a slide of 2.8% the previous month but extending a 1-1/2-year-long stretch of declines.

On Friday, China's central bank said it would make monetary policy flexible, precise and effective and promote a moderate recovery in consumer prices to consolidate economic recovery.

The comments in a quarterly monetary policy report follow remarks in April by the Politburo, a top-decision making body of the ruling Communist Party, that China will use policy tools, such as banks' reserve requirement ratio (RRR) and interest rates, to prop up growth.

"Considering the judgment of the Politburo meeting that 'effective demand is still insufficient...' the policy support should take advantage of the momentum, by strengthening expectation management and creating more consumption scenarios," said Bruce Pang, chief economist China at Jones Lang LaSalle.

Many analysts say China's economic growth target of about 5% in 2024 will be a challenge to achieve without further policy support. (Reporting by Joe Cash and Qiaoyi Li; Editing by William Mallard and Clarence Fernandez)