* Iron ore stock rose to 140.45 mln, just below June peak
* Steel inventories also build, add to price pressure
BEIJING, July 24 (Reuters) - China's iron ore futures fell for a third session on Monday amid increasing concern over surplus supply.
"High inventory has been putting pressure on iron ore prices. Unstable steel prices also helped to curb the margins on raw materials," analysts at Orient Futures wrote in a note.
Stockpiles of imported iron ore at Chinese ports SH-TOT-IRONINV rose by 750,000 tonnes over the last week to 140.45 million tonnes, data from SteelHome consultants showed on Monday, just below a peak of 141.5 million tonnes hit last month that is the highest since at least 2004.
The steelmaking raw material is also piling up at mills. Small- to medium-sized mills are on average holding about 26 days of production, up from 25 days, Orient Futures said.
The most-active iron ore futures on the Dalian Commodity Exchange DCIOcv1 fell 1.5 percent to 509 yuan ($75.30) a tonne during morning trade, after dipping as low as 502 yuan.
Stocks of rebar SH-TOT-RBARINV , mostly used in construction, added 2.34 million tonnes over the last week to 372.7 million tonnes, according to the SteelHome data.
The most-traded steel rebar contract on the Shanghai Futures Exchange SRBcv1 gained 0.26 percent to 3,515 yuan a tonne.
The rise follows a two-day fall of nearly 4 percent at the end of last week as buyer cashed in over concerns about surplus supply.
Spot rebar prices also reflected the supply concerns, losing 0.4 percent on Friday to 3,929.83 yuan a tonne, according to Mysteel data.
($1 = 6.7616 Chinese yuan)