* Hedland port moves record China iron ore shipments in June
* As output rises, Chinese inventories swell (Adds price forecast, details on record shipments, more data)
SYDNEY, July 11 (Reuters) - Record iron ore shipments to China moved through Australia's Port Hedland terminal in June, as major producers BHP Billiton BHP.AX BLT.L and Fortescue Metals FMG.AX operated close to full capacity and inventories at Chinese ports swelled.
Most of the ore both companies mine is sent to China, where higher-grade imports are displacing lower quality domestic ore in Chinese steel mills.
Shipments to China from the Indian Ocean port increased to 34.5 million tonnes in June from 31.7 million tonnes in May, topping the previous record of 33.9 million tonnes in March, according to the Pilbara Ports Authority.
Inventories of imported iron ore at major Chinese ports stood at 104.5 million tonnes on July 11, the most since December 2014, according to data tracked by SteelHome consultancy SH-TOT-IRONINV .
Total iron ore shipments from the port- the world's largest of its kind - climbed to 41.8 million tonnes in June, also a record, from 39.4 million tonnes in May, port data showed.
Since December, the Roy Hill mining partnership of Gina Rinehart's Hancock Prospecting, Marubeni 8002.T , POSCO 005490.T and Taiwan's China Steel Corp 2002.TW have used Port Hedland, joining BHP and Fortescue Metals and contributing to the increase in ore shipments.
The Roy Hill mine will eventually produce up to 55 million tonnes per year, but it will be early next year before that level of production is reached.
Rising production amid a drop in Chinese steel production led Australia's official forecasting agency on Friday to cut its 2016 price forecast by nearly 2 percent to $44.20 a tonne, citing concerns over slowing growth in demand, and it sees little change in 2017. is well below the current price of $55.20 a tonne .IO62-CNI=SI and the first-half average of $48.
China's iron ore mine production fell by 6 percent from a year ago in the first four months of 2016 and is forecast to fall by 12 percent in 2016 and by a further 20 percent in 2017, Australia's Department of Industry, Innovation and Science said in its latest commodity forecast on Friday.