* China commodities track recovery in oil, agriculture
* Steel, iron ore still down about a third from April peaks (Recasts, updates prices)
By Manolo Serapio Jr
MANILA, May 26 (Reuters) - Chinese steel and iron ore futures climbed off 12-week lows on Thursday as commodities traded in the world's top importer of raw materials rebounded, tracking gains in oil and commodities elsewhere.
Cotton, soymeal and rapeseed meal futures in China rallied around 5 percent, while rubber and palm olein rose about 3 percent.
But the outlook for these commodities, led by steel and iron ore, remains shaky in the face of high supply.
Chinese steel and iron ore futures have fallen nearly a third from their peaks in April when a rally pinned largely on retail investors boosted volumes sharply and prompted regulators to impose curbs to restore calm.
The most-traded rebar on the Shanghai Futures Exchange closed up 0.6 percent at 1,953 yuan ($298) a tonne, after falling to as low as 1,907 yuan, its lowest since March 4.
The construction steel product has lost 30 percent from its peak in April.
Steel demand in China "is not that bad" given the signs of recovery in the property sector, said Helen Lau, an analyst with Argonaut Securities in Hong Kong.
"The market's very concerned about steel mills that have restarted and adding to the oversupply," said Lau.
A surge in Chinese steel prices earlier this year, hitting 19-month highs in April, pushed once-shut mills to reopen. But the ensuing retreat in prices could force them to rethink.
On the Dalian Commodity Exchange, iron ore closed 0.7 percent lower at 345 yuan a tonne, off a low of 338 yuan, its weakest since March 1. The contract has fallen 31 percent from its April high.
Other China-traded commodities, mostly agricultural products, outperformed, recovering from recent losses. Cotton on the Zhengzhou Commodity Exchange jumped 5 percent and rapeseed meal rose 4.6 percent.
Dalian soymeal climbed 4.7 percent, palm olein gained 3 percent and Shanghai rubber rose 2.7 percent.
The gains followed a surge in U.S. soymeal futures to an 18-month peak and as Brent crude topped $50 a barrel for the first time since November.
Iron ore for immediate delivery to China's Tianjin port .IO62-CNI=SI slipped 0.4 percent to $50 a tonne on Wednesday, the lowest since Feb. 29, according to The Steel Index. The spot benchmark has fallen 27 percent from a 15-month high reached in April.
"Short of China printing better PMI, it's going to get more challenging. Iron ore in the high $40s, low $50s seems right going forward," Peter O'Connor, analyst for Shaw and Partners in Sydney.
China's official purchasing managers' index (PMI) showed factory activity expanded for the second month in a row in April but only marginally, while a private survey showed manufacturing PMI posting 14 straight months of sector contraction.
$1 = 6.5597 Chinese yuan Reporting by Manolo Serapio Jr.; Editing by Richard Pullin and Subhranshu Sahu