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* Dalian iron ore rises as much as 2.4 pct, Shanghai rebar 1.3 pct
* Iron ore demand from midsize Chinese mills healthy - trader
* China July HSBC services PMI at lowest in nearly nine years (Updates prices)
By Manolo Serapio Jr
SINGAPORE, Aug 5 (Reuters) - Steel and iron ore futures in China climbed to their highest levels in more than two weeks on Tuesday, buoyed by hopes that government efforts to stimulate the economy would spur demand for the two commodities.
China has since April been steadily fuelling economic activity by reducing the amount of cash that some banks have to hold as reserves to increase lending, instructing regional governments to quicken spending, and hastening the construction of railways and public housing.
Chinese steel and iron ore futures stretched gains from Monday even as equities retreated after racing to 7-1/2-month peaks after a dismal survey on the country's services sector.
The HSBC/Markit China services purchasing managers' index fell to 50 in July, the lowest reading since November 2005, indicating a recovery in the broader economy is still fragile and may need further government support.
The most-traded rebar contract for January delivery on the Shanghai Futures Exchange hit a session peak of 3,123 yuan ($506) a tonne, its highest since July 17. It finished up 0.6 percent at 3,102 yuan.
Iron ore for delivery in January on the Dalian Commodity Exchange, the most active contract, rose to 692 yuan a tonne, a level last seen on July 18, before also paring gains at the close to 684 yuan, up 1.2 percent.
While supply from top Australian and Brazilian miners remains brisk "demand from Chinese mills is also quite healthy", said a Shanghai-based iron ore trader.
"There's no lack of offers in the market but we continue to see interest from medium-sized mills to buy forward cargoes," he said.
Some bigger mills were still offloading cargoes from their long-term contracts, said the trader who sold two capesize iron ore cargoes on behalf of mills in northern China in July and is working on another cargo this month.
Top miner Vale is offering to sell via a tender 42,111 tonnes of 63.17 percent-grade iron ore arriving in China in early September, traders said.
Stocks of imported iron ore at China's ports fell for a second straight week to 111.55 million tonnes on Aug. 1, according to industry consultancy SteelHome.
The level has dropped from a record high 113.7 million tonnes reached in early July but remained 29 percent up for the year.
Commonwealth Bank of Australia said there needs to be "a more substantive decrease in port stocks to outweigh the supply impulse coming through at the moment".
"We expect iron ore prices to firm later in the year but in the short term believe it will struggle to lift without a stronger turnaround in the levels of iron ore port stocks," the bank said in a note.
Iron ore for immediate delivery to China .IO62-CNI=SI rose 0.2 percent to $95.40 a tonne on Monday, according to data compiled by Steel Index. Rebar and iron ore prices at 0703 GMT Contract Last Change Pct Change SHFE REBAR JAN5 3102 +18.00 +0.58 DALIAN IRON ORE DCE DCIO JAN5 684 +8.00 +1.18 SGX IRON ORE FUTURES AUG 96.5 +0.33 +0.34 THE STEEL INDEX 62 PCT INDEX 95.4 +0.20 +0.21 METAL BULLETIN INDEX 95.17 -0.67 -0.70 Dalian iron ore and Shanghai rebar in yuan/tonne Index in dollars/tonne, show close for the previous trading day
1 US dollar = 6.1756 Chinese yuan Editing by Muralikumar Anantharaman and Anupama Dwivedi