* Spot iron ore has lost almost 4 pct this week
* Shanghai rebar falls to nearly two-week low
By Manolo Serapio Jr
MANILA, June 17 (Reuters) - Shanghai steel futures fell to two-week lows on Friday, pressured by weak Chinese demand that is also limiting appetite for iron ore, with spot prices of the raw material on course for their third weekly fall in four.
Many Chinese mills may undertake their annual maintenance and repair during the seasonally soft summer period when construction activity slows down, traders said.
"There's more downward pressure for iron ore prices in summer," said a Shanghai-based iron ore trader who has yet to clinch a deal this month.
Iron ore for immediate delivery to China's Tianjin port .IO62-CNI=SI was flat at $50.20 a tonne on Thursday, according to latest available data from The Steel Index.
Still, the spot benchmark has lost 3.6 percent so far this week.
There was little appetite for physical iron ore cargoes this week, traders say, as Chinese steel prices faltered.
The most-traded rebar, a construction steel product, on the Shanghai Futures Exchange SRBcv1 was down 1.3 percent at 2,058 yuan ($312) a tonne by 0325 GMT, after earlier hitting 2,028 yuan, its lowest since June 6.
Even if China's steel exports remain high in coming months, the increase may not be enough to counter slower demand at home, the Shanghai trader said. That could push mills to curb production after ramping up output earlier this year.
China's crude steel output stood at 70.5 million tonnes in May, just off the record high of 70.65 million tonnes produced in March.
As production rose, so did China's steel exports which have climbed 6.4 percent to 46.28 million tonnes in January-May despite growing anger from overseas rivals towards cheap Chinese steel.
On the Dalian Commodity Exchange, the most-active iron ore DCIOcv1 gained 0.8 percent to 368.50 yuan a tonne.
($1 = 6.5875 Chinese yuan)