* Poor steel demand may prod mills to curb output-trader
* Spot iron ore at near two-month low
* Rio Tinto Q2 iron ore output steady
By Manolo Serapio Jr
SINGAPORE, July 17 (Reuters) - Shanghai steel futures hit contract lows on Tuesday and sellers slashed price offers for iron ore cargoes in top market China as weak steel demand continued to weigh on prices.
Chinese spot steel prices have similarly fallen, raising concern mills, which have been producing at or near record highs at above 2 million tonnes a day, could curb output if price losses stretch.
"There's very poor demand for downstream products which will not support mills keeping their production high," said an iron ore trader in Shanghai.
"They might be cutting production soon that's why they're holding off from buying iron ore."
The most-traded rebar contract for January delivery on the Shanghai Futures Exchange dropped 1 percent to 3,850 yuan ($600) a tonne by 0609 GMT, after falling to as low as 3,848 yuan earlier.
Steel billet sold in the key Tangshan area in China's top steel producing Hebei province fell 70 yuan to 3,500 yuan per tonne on Monday, after dropping more than 100 yuan over the weekend, traders said.
The drop in steel prices hit demand for iron ore, with benchmark iron ore falling the most since early June to its lowest in almost two months.
Iron ore with 62-percent iron content .IO62-CNI=SI fell 2 percent to $130.10 a tonne on Monday, declining for a fourth straight day, based on data from the Steel Index.
"All the mills are not buying anything because the market's falling," said another iron ore trader in Shanghai.
"The big mills should have enough stocks for 20-30 days, and the smaller mills can secure additional stocks from the ports.
Stockpiles of iron ore at major Chinese ports stood at nearly 98 million tonnes at the end of last week.
Price offers for imported iron ore cargoes in China dropped by $2-$3 per tonne on Tuesday, according to industry consultancy Umetal.
"Sellers are willing to give discounts on cargoes, but the problem is we don't have firm interest on any of the cargoes. A lot of the buyers have withdrawn their interest to buy," said the second trader.
Miner BHP Billiton is selling 110,000 tonnes of 57.5-percent grade Australian Yandi iron ore fines at a tender on Tuesday.
The first Shanghai trader expects BHP to sell the cargo at below $120 a tonne, against recent done deals at $122.
Rival Rio Tinto reported its iron ore output in the second quarter nearly matched the year-ago volume, but said it was sticking to its full-year production guidance of 250 million tonnes.
"The production guidance is relatively bullish, so we'll have to see how much they're able to sell because the market is a bit oversupplied at the moment," Helen Lau, senior commodities analyst at UOB-Kay Hian in Hong Kong.
"The incentive for Chinese mills to produce more steel is limited because demand is weak and we don't expect a quick recovery because China still has a tightening stance towards the property sector."
Shanghai rebar futures and iron ore indexes at 0609 GMT
Contract Last Change Pct Change
SHFE REBAR JAN3 3850 -39.00 -1.00
PLATTS 62 PCT INDEX 131.5 -2.50 -1.87
THE STEEL INDEX 62 PCT INDEX 130.1 -2.70 -2.03
METAL BULLETIN INDEX 133.95 -0.61 -0.45
Rebar in yuan/tonne
Index in dollars/tonne, show close for the previous trading day
($1 = 6.3787 Chinese yuan)