* Iron ore, steel futures down nearly a third from April peaks
* Coking coal, coke fall more than 2 pct (Recasts, updates prices)
By Manolo Serapio Jr
MANILA, May 25 (Reuters) - Iron ore and steel futures in China dropped to 12-week lows on Wednesday, reflecting further pressure in glut-hit markets that have fallen nearly a third from last month's peaks.
Softening demand for steel in China, the world's top consumer, following a seasonal pickup could push mills to curb production again, traders said.
Many mills shut down over the past year in response to weak demand and some of them resumed output as prices rallied in April. might see some cut in production, even from the big state-owned mills," said an iron ore trader in Shanghai.
Rebar, or reinforcing bar used in construction SRBcv1 , closed down 1.3 percent at 1,916 yuan ($292) a tonne on the Shanghai Futures Exchange. It touched 1,912 yuan earlier, the lowest since March 4.
Rebar has fallen more than 31 percent from its highest point in April when a rally fueled by faith in China's economy, low inventories and seasonal demand pushed rebar to its highest since September 2014.
It was an upsurge that spilled over to iron ore and other commodities and trading volumes shot up massively that exchanges had to slap curbs to restore order in markets. coil SHHCcv1 , used in cars, fell 1.1 percent to 2,105 yuan a tonne. Open interest, or open contracts, in hot-rolled coil futures in Shanghai surged to a record 254,166 lots as prices fell 29 percent from April highs.
As steel prices fall back sharply and Chinese mills incur losses again, producers "will either begin working down their own iron ore inventory or pulling back production until steel prices are once again supportive," analysts at Liberum Capital said in a note.
"Either way the apparent iron ore demand will fall and drag on prices."
Iron ore on the Dalian Commodity Exchange DCIOcv1 closed 2.2 percent lower at 342 yuan a tonne, after hitting 340 yuan, its weakest since March 1.
That could pull spot prices further. Iron ore for immediate delivery to China's Tianjin port .IO62-CNI=SI slid 4.7 percent to $50.20 a tonne on Tuesday, the lowest since Feb. 29, according to The Steel Index. It has fallen 27 percent from its April high.
Other steelmaking commodity futures also slipped, with Dalian coking coal DJMcv1 down 2.2 percent and coke DCJcv1 falling 2.6 percent.
($1 = 6.5585 Chinese yuan)