MELBOURNE, July 29 (Reuters) - Origin Energy, a co-owner of the Australia Pacific LNG project, said APLNG's sales volumes rose 28 percent but prices fell 15 percent in the June quarter, and the project was on track to start shipping from its second unit by December.

APLNG, operated by ConocoPhillips, exported its first cargo in January and to date has shipped 32 cargoes, including the first to Japan's Kansai Electric Power Co , Origin said in its quarterly report on Friday.

"The Train 1 LNG facility continues to perform to expectations, with daily production rates having achieved and exceeded design nameplate capacity," Origin said. The unit's rated capacity is 4.5 million tonnes a year.

It reaffirmed that the plant's second unit is expected to ship its first cargo in the current half year.

Average LNG prices fell to $5.23 per million Btu (mmBtu) in the June quarter from $6.17 in the March quarter, it said.

Origin Energy supplies gas from coal seam gas wells in Queensland to the APLNG plant, which helped boost the company's revenue by 15 percent to A$1.08 billion ($813 million) in the year to June 2016 from a year earlier.

Its annual production soared 57 percent to 231.5 petajoules equivalent, mostly due to the start-up of APLNG.

($1 = 1.3282 Australian dollars) (Reporting by Sonali Paul; Editing by Biju Dwarakanath)