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* China May industrial profits +0.7% y/y vs 4% in April

* Soft domestic demand crimps business activity

BEIJING, June 27 (Reuters) - China's industrial profits rose at a much slower pace in May, official data showed on Thursday, underlining the struggles faced by the world's second-largest economy as weak domestic demand crimps overall growth.

Earnings rose 0.7% year-on-year last month after a 4% increase in April while gains over the first five months also eased to 3.4% from 4.3% in the January-April period, according to National Bureau of Statistics (NBS) data.

The closely watched gauge of business conditions follows a flurry of largely downbeat economic indicators in May. While exports were strong, the property sector has failed to respond to a "historic" rescue packaged announced last month. “Effective domestic demand remains insufficient ... and the foundation for recovery of industrial profits" isn't solid as yet, NBS statistician Yu Weining said in an accompanying statement.

Yu attributed the slower growth to "short-term factors including a decline in investment proceeds growth."

The automobile industry, a major contributor to consumer discretionary growth, had a profit margin of 4.6% in the first four months, underperforming an average of 5% in the overall factory sector, data from the China Passenger Car Association showed earlier in June.

The automakers rely on exports and upscale models for most of their profits amid intense competition at home and many of them have seen a drastic decline in earnings, the association said.

China's state planner on Monday encouraged local governments to loosen car purchase restrictions, in the latest slew of measures to prop up weak domestic demand, which alongside rising tensions with the West put pressures on businesses.

State-owned firms posted a 2.4% drop in profits in the first five months, foreign firms tallied a 12.6% gain, while private-sector companies saw profits up 7.6%, according to a breakdown of the NBS data.

Industrial profit numbers cover firms with annual revenue of at least 20 million yuan ($2.76 million) from their main operations. ($1 = 7.2388 Chinese yuan) (Reporting by Qiaoyi Li and Ryan Woo Editing by Shri Navaratnam)