Further upside for palm oil prices will be limited, as harvest in South East Asia reaches its seasonal peak, Anglo-Eastern Plantations said.
But there is potential for a rally, if soyoil supplies tighten due to the effects of a potential La Nina phenomenon, according to the Indonesia based palm oil producer.
"The recovery of price since the beginning of the year was due to the decline in CPO production brought on by the drought from last year," Anglo-Eastern said.
"The upside of crude palm oil price is limited as the industry heads into its peak production cycle in the third quarter of 2016," the company warned.
Anglo Eastern reported a sharp drop in profits and sales, citing the effects of a palm oil export tax in Indonesia, and lower production.
"But as the El Nino weather phenomenon dissipated, weather forecasters globally are predicting a 50-75% chance of La Nina developing in the second half of 2016," said Anglo Eastern.
"The emergence of La Nina and resultant rains in the region could help improve [fruit] yields."
And Anglo Eastern said that a La Nina effect would bring "extreme dryness to the eastern side of the Pacific," potentially hitting soybean yields in the Americas.
Such a development would make palm oil more competitive against soybean oil, supporting prices.
"If La Nina develops, it could potentially see crude palm oil price strengthen in the fourth quarter of 2016 especially in the wake of a wider discount to soybean oil," Anglo-Eastern said.
Palm oil and soyoil are readily substituted for each other, leading to a strong price correlation.
On Thursday the US broker CHS Hedging noted that the recent break in palm oil prices has dragged soyoil off its recent peak.
"Soy oil has rallied for most of August gaining support from a strong palm oil market.
Production of palm oil fruit at Anglo-Eastern's plantations was down 3% year on year, at 378,400 tonnes.
"The decline in production, in spite of an increase in matured area, was mainly attributed to the replanting of old palms in North Sumatera," said Anglo-Eastern.
But crop yields in while lower crop yield was evident in Riau, in Central Sumatra, and Kalimantan in Borneo, were affected by las year's drought.
"It was reported that plantations across Indonesia faced production decline, some up to 20% for a similar reason," Anglo-Eastern said.
Anglo-Eastern's off-plantation purchase were hit by this dry weather, with bought in crops down by 22%, to 264,500m tonnes, due to "dry weather and intense competition particularly at its mill in Riau".
Anglo-Eastern reported revenues down 17% year on year in the first six months of 2016, at $86.0m, despite a rise in crude palm oil prices.
The company noted that despite palm oil prices in Rotterdam averaging $668 a tonne, $5 a tonne higher than in the first half of 2015, returns fell due to an export levy of $50 a tonne, imposed by Indonesian government in July.
Pre-tax profits fell by 10% year on year, to $19.5m, over the six month period.
Anglo Eastern shares in London were up 5.1% in afternoon deals, at 22.50 pence.