The benchmark palm oil contract for September delivery on the Bursa Malaysia Derivatives Exchange was up 1.2pc at 2,047 ringgit ($491) per tonne at the close.
Cargo surveyors and an independent inspection company had over Saturday and Monday reported more than 15pc falls in exports for the June 1-15 period.
"The export rumour for June 1-20 period shows better numbers than in the earlier period," a futures trader based in Kuala Lumpur said.
Malaysia's Southern Peninsular Palm Oil Millers Association reported a 26.4pc drop in production on Monday which also helped boost prices.
In other related oils, the Chicago July soybean oil contract was last up 0.5pc.
The September soyoil contract on the Dalian Commodity Exchange fell 1.2pc and the Dalian September palm oil contract was also down 0.2pc.