* Steel and iron ore futures at 7-week lows
* Steady supply, slow demand pick-up hurt expectation
* China August steel output rises for 6th straight month
SHANGHAI, Sept 13 (Reuters) - Chinese steel futures stretched losses to a seven-week low on Tuesday on worries over demand in the world's top producer, dragging down prices of raw material iron ore.
Concerns over a slow recovery in demand after the summer construction lull amid steady supplies of steel have raised concerns that prices could come under further pressure.
"The rise in August was driven by expectations that demand would pick up in September but the reality is we haven't seen any boost in buying for now," said Xia Junyan, an investment manager of Hangzhou CIEC Trading Co in Shanghai.
China has made increased efforts to cut steel overcapacity, toughening its stance in an environmental crackdown and shutting many smaller mills. However, analysts expect the government will work to meet its annual target, but won't exceed it.
"The production interruptions lifted sentiment earlier, and now the market does not have any stories to trade," Xia said.
China promised to slash steel capacity by 45 million tonnes this year and cuts in the first seven months of the year amounted to 47 percent of the annual target, spurring Beijing to vow to quicken its pace. most active futures contract for construction product rebar on the Shanghai Futures Exchange SRBcv1 hit a session low of 2,264 yuan ($339.38) a tonne, its lowest since July 25. It traded 1.8 percent lower at 2,265 yuan by the midday break.
China's crude steel output rose 3 percent in August from a year ago, the sixth straight monthly rise and the latest sign that a rally in prices and pick-up in demand spurred mills in the world's top producer to ramp up output. the Dalian Commodity Exchange, the benchmark iron ore futures contract DCIOcv1 fell 3.1 percent to 392.5 yuan a tonne by midday, earlier touching its lowest since July 27.
($1 = 6.6798 Chinese yuan renminbi)