* Chinese stocks fall sharply on economy worries
* Iron ore futures in China, Singapore drop
* Spot iron ore slips from 10-week high (Adds China stocks, updates prices)
By Manolo Serapio Jr
MANILA, Sept 15 (Reuters) - Iron ore futures in China slid more than 3 percent on Tuesday and those in Singapore also dropped along with Chinese steel prices as investors sold off risky assets on persistent worries over a slowing economy.
China's equities led the slide, with key indexes falling about 4 percent. .SS
Iron ore for January delivery on the Dalian Commodity Exchange DCIOcv1 , the most traded contract, closed down 3.2 percent at 392.50 yuan ($62) a tonne, pulling further away from Friday's 10-week high of 417 yuan.
The October contract on the Singapore Exchange SZZFV5 slipped 1.3 percent to $53.46 a tonne.
"Steel demand is not great I agree, but mills keep producing and as long as you keep producing you keep pressure on steel prices," said an iron ore trader in Shanghai.
Steel consumption in China, the world's top consumer, has continued to shrink after dropping in 2014 for the first time in more than three decades, and this year, the market remains oversupplied, forcing many producers to sell more overseas.
The most-active January rebar on the Shanghai Futures Exchange SRBcv1 dropped 1.3 percent to 1,909 yuan a tonne.
The sustained steel production should support iron ore prices, traders said, which have largely stabilised above $50 a tonne since recovering from a decade-low of $44.10 in July.
Iron ore for immediate delivery to China's Tianjin port .IO62-CNI=SI fell 1.7 percent to $57.50 a tonne on Monday, reported the Steel Index (TSI), citing a large gap between bids and offers on physical trading platforms in China and Singapore.
"Some traders were holding out for higher prices privately, but buyers shied away," price assessment agency TSI said.
"I don't think there's too much room for prices to go down.
There should be some stock buildup by mills before the October holidays," said the Shanghai trader, referring to the week-long National Day holiday in China.
Stocks of iron ore in the country are also not high, indicating steady demand among mills.
Iron ore inventory at 44 Chinese ports stood at 80.05 million tonnes as of Sept. 11, the lowest since late June, data from consultancy SteelHome showed. SH-TOT-IRONINV
China's iron ore output dropped 9.5 percent in August from a year ago to 123.81 million tonnes, government data showed. MTL/CHINA7
Rebar and iron ore prices at 0701 GMT
Contract
Last
Change Pct Change SHFE REBAR JAN6
1909
-26.00
-1.34 DALIAN IRON ORE DCE DCIO JAN6
392.5
-13.00
-3.21 SGX IRON ORE FUTURES OCT
53.46
-0.72
-1.33 THE STEEL INDEX 62 PCT INDEX
57.5
-1.00
-1.71 METAL BULLETIN INDEX
58.1
-0.91
-1.54
Dalian iron ore and Shanghai rebar in yuan/tonne Index in dollars/tonne, show close for the previous trading day ($1 = 6.3675 Chinese yuan) (Editing by Tom Hogue and Anand Basu)