COCOA
July London cocoa rose by 36 pounds, or 2.4 percent, to 1,531 pounds a tonne by 1020 GMT.
Dealers said the market had rebounded strongly after suffering its biggest one-day fall since 2011 on May 24.
The decline had been fuelled by excess supplies linked to a huge crop in top grower Ivory Coast and bearish chart signals.
"Friday's (stronger) performance and today so far may suggest that the market has had its fill of bear news and we might enter a period of consolidation and maybe build a base," one London dealer said.
Dealers said the market may also have derived some support from heavy rains in Ivory Coast.
Abundant rainfall last week in most of Ivory Coast's main cocoa-growing regions sparked fears that flooding could hinder harvesting of what is otherwise expected to be a strong mid-crop, farmers said on Monday.
July New York cocoa was up $55, or 2.88 percent, at $1,966 a tonne.
SUGAR
July raw sugar fell 0.18 cents, or 1.2 percent, to 14.87 cents per lb after dipping to a low of 14.84 cents, its weakest since April 2016.
Dealers said that bearish factors included more favourable crop weather and a recent cut in gasoline prices in top grower Brazil while monsoon rains could improve the outlook for crops in India, the world's second-biggest producer.
Crop-nourishing monsoon rains lashed the Kerala coast of India's southwest on Tuesday, the India Meteorological Department said, in the earliest start to the rains since 2011.
August white sugar fell by $3.90, or 0.89 percent, to $435.30 a tonne.
COFFEE
July robusta coffee was down $7, or 0.35 percent, at $1,984 a tonne.
Dealers said the market was struggling to overcome resistance around $2,000 that has stalled its recent advance.
"If futures failed to take out $2,000 this may lead to a test of support at the 50 percent fib (Fibonacci) level at $1,956," Sucden Financial research analyst Geordie Wilkes said in a market note.
July arabica rose 0.4 cents, or 0.3 percent, to $1.3160 per lb.