* Bullish trend continues as short-sellers cover positions
* Open interest in iron ore rebounds as long positions build
* Rebar hits highest level since December 2013 at 3,688 yuan/T (Updates prices)
BEIJING, July 19 (Reuters) - China's iron ore futures rose for a third session on Wednesday, hitting their highest in 2-1/2 months, as speculators added bullish bets and shorts continued to cover their positions betting on higher prices on strong demand from steel mills.
"Some short-position investors have pulled out of iron ore, helping to push prices up. If spot prices can move upward, the September iron ore contracts is expected to extend gains," CITIC Futures analysts wrote in a research note in Chinese.
The most-active iron ore futures contract DCIOcv1 closed 3.7 percent higher on Wednesday at 532 yuan a tonne, its highest since May 3.
Open interest in the most-active iron ore futures contract eased by 177,000 lots to 1.66 million lots, equivalent to 166 million tonnes worth 88.3 billion yuan ($13.07 billion) by Wednesday afternoon.
That reflects continued short covering that started last week. Traders said speculators have taken that as a cue for them to increase their net longs after data on Monday showed steel mills churned out record volumes of metal in June, spurring hopes of restocking for raw materials by producers. has been recovering after touching 2.3 million lots, its lowest in seven weeks on Friday last week.
The most-traded steel rebar contract on the Shanghai Futures Exchange SRBcv1 extended its recent rally, rising 1.8 percent to 3,679 yuan a tonne, after touching 3,688 yuan in the morning session, its highest since December 2013.
"The market is optimistic toward the rallying prices on steel products, since the inventory remains at a low level," analysts at Orient Futures wrote in a note.
Stocks of rebar held by Chinese traders SH-TOT-RBARINV dropped 1 percent to 370.4 million tonnes on Monday, the lowest since December 2016, SteelHome data showed.
Spot rebar rose 0.34 percent to 3,932.59 yuan a tonne on Tuesday, according to data on the Mysteel Consultancy website.
($1 = 6.7560 Chinese yuan)