* Shanghai rebar, Dalian iron ore come off session highs
* Spot iron ore stays above $80/tonne
By Manolo Serapio Jr
MANILA, March 30 (Reuters) - Shanghai rebar steel futures rose for a third session on Thursday, supported by China's campaign to eliminate surplus capacity, although concerns over tepid seasonal demand capped their upside.
The gains helped iron ore recover further from an early-week slide that pulled down futures to their weakest in more than two months and spot prices to their lowest in seven weeks.
But both steel and iron ore futures have come off the day's peaks, suggesting still shaky investor sentiment.
The most-active rebar on the Shanghai Futures Exchange was up 0.7 percent at 3,147 yuan ($457) a tonne by 0311 GMT, after earlier peaking at 3,189 yuan. The construction steel product touched 3,003 yuan on Monday, its weakest since Feb. 10.
"China's ongoing efforts in reducing outdated capacity, constraining steel production and regulating pollutant emissions will tighten the steel market, supporting steel prices going forward," Argonaut Securities analyst Helen Lau said in a note.
China's Hebei province, a major steel-producing area, has launched a fresh probe into steel overproduction in the city of Tangshan amid concerns that firms have continued to raise output despite mandatory capacity cuts.
The northeastern Chinese province of Liaoning has promised to close more than 10 million tonnes of low-grade steel capacity by the end of June as part of its efforts to clean up the sector, the official Liaoning Daily reported on Tuesday.
Iron ore for September delivery on the Dalian Commodity Exchange was last up 0.8 percent at 566 yuan per tonne, well off a session high of 581.50 yuan. The contract on Monday touched its lowest since Jan. 10 at 541 yuan.
The towering stocks of imported iron ore at China's ports which underline slow demand for the steelmaking raw material has put prices under pressure.
Port inventory reached 132.45 million tonnes on March 24, the most since at least 2004, according to SteelHome consultancy. SH-TOT-IRONINV
Iron ore for delivery to China's Qingdao port .IO62-CNO=MB edged up 0.3 percent to $82.25 a tonne, according to Metal Bulletin. ($1 = 6.8944 Chinese yuan) (Reporting by Manolo Serapio Jr.; Editing by Joseph Radford)