* Shanghai rebar extends decline, hits record low
* Iron ore also falls; benchmark TSI at $125/T
* Traders see prices dropping further on weak demand (Adds detail, comment from trader)
SHANGHAI/BEIJING, July 23 (Reuters) - China steel futures fell over 2 percent on Monday to a record low of around 3,650 yuan ($570) a tonne, with their outlook darkened by high stockpiles and tepid demand.
The most-traded January Shanghai rebar futures hit a fresh contract low of 3,652 yuan a tonne, after falling 3.6 percent last week. The contract was down 1.2 percent by 0206 GMT.
The price of rebar, used in construction, has been declining steadily since early July and is on track to fall over 7 percent this month. That would mark its steepest monthly decline since September 2011.
Although Beijing has recently fast-tracked some infrastructure investments, with Chinese Premier Wen Jiabao pledging to boost the country's economy, steel traders are doubtful there will be any moves that will significantly prop up steel demand.
"Obviously we are hoping that there will be some stimulus from the government but I personally don't think we will get anything soon - they are just relying on measures like interest rates to try to improve demand," said a manager with an international iron and steel trading firm in Beijing.
"I think prices will actually get lower than this because there are no good signs for the market."
Steel product stocks held by traders in China climbed 26 percent from a year ago to 6.71 million tonnes, according to data from consultancy Mysteel.
A firm reminder by Beijing to local governments to keep clamping down on property speculation, also weighed on sentiment.
Poor demand for steel in China, the world's largest producer, has also spilled over to the iron ore market, with benchmark 62-percent grade ore .IO62-CNI=SI falling for the eighth consecutive day on Friday to $125 a tonne.
"With steel prices still in free-fall, the iron ore market continued to look incredibly weak as buyers and sellers withdrew to the sidelines," the Steel Index said in its weekly report.
Still, some participants hope that declining steel prices could erode steel makers' profit margins and force them to cut production, which would help reduce the massive supply overhang in the market and stabilise prices.
"That would be a great thing for the market - but I'm not sure if it will happen," said the trader.
China's daily crude steel output averaged 1.958 million tonnes in the first 10 days of July, down 0.4 percent from the preceding 10-day period, industry data showed this week.
($1 = 6.3735 Chinese yuan)