* Rising steel supply suggests any price gains may be fleeting
* Iron ore stocks at China ports highest since Dec 2014 (Recasts, updates prices)
By Manolo Serapio Jr
MANILA, July 7 (Reuters) - Chinese steel futures trimmed gains on Thursday and iron ore fell back as worries over a steel glut in the world's top consumer and producer kept the two commodities under pressure.
The most-traded rebar, a construction steel product, on the Shanghai Futures Exchange SRBcv1 closed 0.7 percent higher at 2,387 yuan ($357) a tonne after rallying as much as 3.6 percent.
The big gains earlier were in line with a recovery in risk appetite across Asia following Wednesday's selloff that was spurred by renewed fears on the global impact of Britain's exit from the European Union.
On the Dalian Commodity Exchange, steelmaking raw material iron ore DCIOcv1 slipped 0.6 percent to end at 426.50 yuan a tonne, after rising as far as 439 yuan.
Richard Lu, analyst at CRU consultancy in Beijing, said there has been no significant changes in supply-demand dynamics.
"This is largely sentiment driven," said Lu. "The market will eventually be taken hold of again by fundamentals particularly in the longer term and I expect that there will be a downward correction in the futures market."
China is under pressure from other countries, led by the United States, to cut it excess steel capacity, estimated at around 300 million tonnes or three times Japan's annual output.
Cheap steel shipments from China have forced countries to impose a slew of anti-dumping duties against Beijing.
The recent spikes in Chinese steel prices have encouraged northern Chinese mills to boost output, said Lu, adding to the glut.
While recent severe flooding across central and southern China should curb production among mills located there, Lu said "simultaneously demand from these regions will also be seriously impacted".
Traders say there has been limited activity in the spot iron ore market amid plentiful stocks of the raw material at China's ports.
Iron ore for delivery to China's Tianjin port .IO62-CNI=SI was nearly flat at $55.80 a tonne on Tuesday, according to The Steel Index. The price assessor did not publish prices on Wednesday due to the Singapore public holiday.
Inventory of imported iron ore at major Chinese ports stood at 102.55 million tonnes on July 1, the most since December 2014, according to data tracked by SteelHome consultancy SH-TOT-IRONINV .
($1 = 6.6850 Chinese yuan)