The benchmark palm oil contract on the Bursa Malaysia Derivatives Exchange was down 1.2pc at 1,997 ringgit ($482.60) per tonne at the close, the largest intra-day drop since June 12.
The most-active Chicago Board of Trade soyoil futures were 0.3pc lower, while China's Dalian soybean oil prices were down 0.9pc.
"Rumour of poorer exports are weighing on palm, and soyoil prices are also dropping," said one Kuala Lumpur-based trader.
Another trader added that demand was slow, topped with concerns that US-Iran tensions could worsen demand.
Crude oil prices climbed on Monday as tensions remain high between Iran and the United States, with US Secretary of State Mike Pompeo saying "significant" sanctions on Tehran would be announced.
Palm oil looks neutral in a range of 2,001-2,046 ringgit per tonne, and an escape could suggest a direction, according to
Wang Tao, a Reuters analyst for commodities technicals.
The range is formed by the 76.4pc and the 61.8pc projection levels of a downward wave C from 2,235 ringgit.
A break above 2,046 ringgit could lead to a gain to 2,082 ringgit.