* Steel futures drop to lowest since July 25
* Iron ore hits lowest since July 27
* Demand yet to seasonal pick-up - traders
* Iron ore inventories remain high (Updates close prices)
SHANGHAI, Sept 12 (Reuters) - Chinese steel futures fell to a seven-week low on Monday amid few signs of a pick-up in demand in the world's top producer and consumer despite expected seasonal strength, while worries over a possible U.S. rate hike dampened commodities more broadly.
The most active rebar futures contract on the Shanghai Futures Exchange SRBcv1 fell as much as 2.3 percent to 2,270 yuan a tonne, its lowest since July 25. It traded 2 percent lower at 2,277 yuan by close.
Steel demand traditionally picks up in September after the summer slowdown, but actual demand has failed to show a recovery since August amid a cooling economy and the suspension of some construction activity for the G20 summit.
"Real demand in August was not as good as July and the G20 summit in Hangzhou hit consumption, so let's see if demand will grow in September," said Li Wenjing, an analyst with Industrial Futures in Shanghai.
On the Dalian Commodity Exchange, the benchmark iron ore futures contract DCIOcv1 fell 2 percent to close at 398 yuan a tonne. It earlier hit a session low of 396.5 yuan a tonne, the lowest since July 27.
Iron ore port inventories CUS-STKTOT-IORE fell 2 percent to 103.75 million tonnes by last Friday, but remain at high levels, sticking above 100 million tonnes since July, industry website Umetal.com showed.
Chinese commodities fell across the board amid expectations that U.S. could consider a rate rise later this month. U.S. Federal Reserve officials are divided on whether a rate rise is in the offing, with some of the permanent voting members appearing wary of supporting an immediate hike. = 6.6790 Chinese yuan renminbi)