* Steel futures hit a one-week high
* Iron ore futures touch a five-week peak
* Mills' orders firm, inventories not piling up (Updates close prices)
SHANGHAI, June 22 (Reuters) - Chinese steel futures rose for a third consecutive session and hit a one-week high on Wednesday, as a pick up in orders by steel mills and the absence of a spike in inventories despite an expected seasonal lull in construction underpinned prices.
The most active rebar futures for October delivery on the Shanghai Futures Exchange SRBcv1 rose 2.8 percent to 2,143 yuan ($325.27) a tonne by close, the highest since June 14.
"Investors have raised hopes that downside risk for prices is small after a big slump in May while steel mills' orders unexpectedly picked up and market inventories did not pile up," said Zhao Chaoyue, an analyst with Merchant Futures in Shenzhen.
Total inventories of five steel products, including hot-rolled coil for machinery use and rebar for construction use, remained unchanged at 8.126 million tonnes in June versus a month ago, the China Iron & Steel Association said on Monday.
Typically, steel stocks pile up as construction work slows down in China between June and August due to hot weather. But this year steel demand in the top consumer has picked up on a year-on-year basis due to China's stimulus measures, Zhao added.
"A couple of mills that I've spoken to have seen their orders picking up in early June from the average level in May when sales were hit by a big slump in prices," Zhao added.
Steel futures tumbled 22 percent in May after a 21 percent jump in April. Demand for the alloy is expected to pick up steam again around September and October.
Tracking gains in steel, the price of raw material iron ore has also risen this week.
Iron ore for immediate delivery to China's Tianjin port .IO62-CNI=SI edged up 10 cents to $50.70 a tonne on Tuesday, data compiled The Steel Index showed.
The September iron ore contract traded on the Dalian Commodity Exchange DCIOcv1 surged 3.5 percent to 386.5 yuan a tonne by close. It earlier touched a five-week high of 388 yuan a tonne. ($1 = 6.5883 Chinese yuan)