* Rebar posts fifth decline in a row
* China's stock market rout stokes fears over economy (Updates closing prices)
SHANGHAI, Aug 20 (Reuters) - Chinese rebar futures fell for a fifth straight session to their lowest in four weeks on Thursday, as a deeper economic slowdown in the world's top steel producer hit demand for industrial metals.
China's equity market rout has fueled fears over problems in its economy, weighing on price prospects in the commodities sector. Copper prices CMCU3 sank to a six-year low this week.
The most active January rebar contract on the Shanghai Futures Exchange SRBcv1 touched a session trough of 2,020 yuan ($315.75) a tonne on Thursday, their lowest since July 23. It closed down 0.44 percent at 2,028 yuan a tonne.
Steep declines in steel prices that have fallen by a quarter since the start of 2015 have forced many steel mills to curtail production, piling pressure on steelmaking ingredient iron ore.
"We have slashed production by one-third due to weak demand and tougher anti-pollution measures," said an iron ore buying official with a steel mill in Shandong province.
"Spot iron ore prices stayed firm, but they remain under pressure in the second half of this year due to the gloomy outlook for steel demand."
For iron ore, the most traded January contract on the Dalian Commodity Exchange DCIOcv1 edged up 0.13 percent to 376 yuan a tonne.
Iron ore for immediate delivery to Tianjin port .IO62-CNI=SI slipped 0.2 percent to $55.90 a tonne on Wednesday, according to The Steel Index.
The Shanghai Composite index .SSEC has lost more than 8 percent since Tuesday, highlighting investors' lack of faith in government efforts to stabilize stock prices ID:nL3N10U351 ($1 = 6.3975 Chinese yuan)