The benchmark palm oil contract for July delivery on the Bursa Malaysia Derivatives Exchange edged down 1 percent to 2,473 ringgit ($560.90) a tonne at the end of the trading day.
It earlier fell to an intraday low of 2,468 ringgit, its lowest levels since Aug. 11.
Traded volumes stood at 59,760 lots of 25 tonnes each on Tuesday evening.
"The market is down on weaker soyoil, and also on continued concerns of higher supplies both in Malaysia and Indonesia," a Kuala Lumpur-based futures trader said.
Production growth in the world's top producers of the tropical oil is forecast to recover between now and the third quarter of the year, as the lingering effects of a crop damaging El Nino wear off.
Malaysian production rose for the full month of March, up 16.3 percent from February, its first monthly gain since September, in line with seasonal trends.
Palm oil prices are also affected by movements in rival edible oils as they compete for a share in the global vegetable oils market.
Soybean oil on the Chicago Board of Trade was down 0.8 percent, while the September soybean oil contract on the Dalian Commodity Exchange fell 1.4 percent.
In other related vegetable oils, the September contract for palm olein declined 1.3 percent.
Palm oil is expected to test a support at 2,484 ringgit, a break below which could cause a further loss into 2,437-2,464 ringgit range, a Reuters market analyst for commodities and energy technicals said.