* Dalian iron ore also recovers from four-month low
* China produced a record 72.78 mln tonnes of steel in April
* Iron ore at China's ports at highest level since at least 2004 (Updates prices)
By Manolo Serapio Jr
MANILA, May 16 (Reuters) - Shanghai rebar steel edged higher on Tuesday after a three-day fall, but gains were limited by concerns over plentiful supply and slow growth in demand in top consumer China.
Optimism for the future lent some support, though, with Chinese President Xi Jinping pledging $124 billion for his new Silk Road plan that aims to expand investments in Asia, Africa and Europe and boost demand for raw materials such as steel.
The most-active rebar on the Shanghai Futures Exchange closed up 0.6 percent at 2,999 yuan ($435) a tonne. The construction steel product hit a one-week low of 2,925 yuan on Monday.
"We remain positive on Chinese steel demand but we also continue to believe Chinese steel output rates are unsustainably high, and will eventually decline," Commonwealth Bank of Australia analyst Vivek Dhar said in a note.
"That should translate through to weaker iron ore demand and prices, too."
China produced a record 72.78 million tonnes of crude steel in April, official data showed on Monday, as mills anticipated stronger demand with the government committed to boost infrastructure spending.
But traders say steel consumption has not been as brisk as many in the market had expected, bloating stocks of raw material iron ore at Chinese ports to the highest in at least 13 years.
Inventory of imported iron ore at 46 Chinese ports reached 134.25 million tonnes SH-TOT-IRONINV on May 12, up 2.3 million tonnes from the previous week, according to data tracked by SteelHome consultancy.
It was the highest such inventory since SteelHome began compiling the data in 2004.
Iron ore on the Dalian Commodity Exchange climbed 1.5 percent to end at 461 yuan a tonne, after touching a four-month trough of 442.50 yuan on Monday.
Iron ore for delivery to China's Qingdao port .IO62-CNO=MB slipped 0.9 percent to $60.80 a tonne on Monday, according to Metal Bulletin. ($1 = 6.8914 Chinese yuan) (Reporting by Manolo Serapio Jr.; Editing by Tom Hogue and Biju Dwarakanath)