* China factory activity hits 7-month low
* Sellers cut iron ore prices offers by $1/tonne
SINGAPORE, July 2 (Reuters) - China steel futures touched one-month lows on Monday, reflecting a sluggish market that has cut the appetite for raw material iron ore and prompted mills in the world's top steel producer to curb output.
Data showing factory activity in China hitting its lowest in seven months is expected to keep the steel demand outlook weak and prices under pressure, as shrinking new orders and the steepest fall in export orders since December suggested no immediate pick up for the world's second-biggest economy.
The most active steel rebar contract for October delivery on the Shanghai Futures Exchange dropped 0.7 percent to 4,039 yuan ($640)a tonne by 0607 GMT. It hit a session trough of 4,028, its weakest since June 4.
The weakness in steel has kept Chinese mills off the spot iron ore market, forcing sellers in China to cut prices for cargoes from Australia and Brazil, the top two exporters, by another $1 per tonne on Monday, data from industry consultancy
"We haven't bought anything over the last week and probably we'll only consider buying if the 62-percent grade falls to around $130," said a Shanghai-based trader.
Benchmark 62-percent grade iron ore .IO62-CNI=SI dropped 0.7 percent to $134 a tonne on Friday, the lowest since June 13, according to Steel Index.
Iron ore ended the second quarter down more than 9 percent despite a 10-day rally in June fueled by traders betting that high steel output would encourage Chinese mills to restock on iron ore.
But declining steel prices, which fell 6 percent in April-June, forced producers to cut output.
China's daily crude steel output from June 11 to 20 dropped 1.4 percent from the preceding 10 days, data from the China Iron and Steel Association showed last week.
"A lot of people in the market had been too optimistic about iron ore before, when there was no change in the steel market's fundamentals," said another trader in Shanghai.
"We are still seeing limited steel demand, so iron ore prices may continue to be soft this week."
Shanghai rebar futures and iron ore indexes at 0607 GMT
Contract Last Change Pct Change
SHFE REBAR OCT2 4039 -29.00 -0.71
PLATTS 62 PCT INDEX 135.25 -1.00 -0.73
THE STEEL INDEX 62 PCT INDEX 134 -0.90 -0.67
METAL BULLETIN INDEX 135.49 -0.55 -0.40
Rebar in yuan/tonne
Index in dollars/tonne, show close for the previous trading day
($1=6.3541 Chinese yuan)