U.S. corn futures rebounded from a six-week low on Tuesday and soybeans also edged higher as a rise in crude oil and many other commodities provided some respite to markets weighed down by plentiful supplies.

May corn on the Chicago Board of Trade was up 0.3 percent at $3.58 a bushel at 1132 GMT. The contract had earlier dipped to a low of $3.56-1/2, its weakest level since Jan. 12.

Commerzbank said in a market update that demand for U.S. corn looked set to fall short of supply in the coming 2016/17 crop year and the stocks-to-use ratio could climb to its highest level in 11 years.

The stocks-to-use ratio for U.S. wheat is also expected to be at "an extremely high level" and for U.S. soybeans at its second-highest level in the last 10 years, the bank said.

"There can be no talk of any risk of tight corn, wheat or soybean supply. As such, prices will remain low for the foreseeable future," Commerzbank said.

Farmer selling in the U.S. is putting further pressure on grain and oilseed markets.

U.S. farmers are offloading some of their massive stocks of corn and soybeans as they seek cash to pay for spring expenses like seed and farmland rent, trade sources said.

CBOT May soybeans rose 0.5 percent to $8.65-1/4 a bushel. The contract had dipped to a low of $8.60 on Monday, its weakest level since Jan. 12 weighed partly by an improving outlook for production in Brazil.

Consultancies França Junior and Agroconsult raised their estimates for Brazil's 2015/16 soybean harvest last week in a sign losses from irregular rain in Mato Grosso last year were not as steep as originally thought.

"Rain is still likely to cause delays at Brazilian ports but, but other than that, crop conditions in South America look largely favorable," said Tobin Gorey, director of agricultural strategy at Commonwealth Bank of Australia in Sydney.

Wheat prices were slightly lower, however, with CBOT May off 0.1 percent at $4.52-3/4 a bushel and May wheat in Paris down 0.3 percent at 154.00 euros a tonne.

Commodity funds sold an estimated net 7,000 CBOT corn contracts on Monday, trade sources said. The funds also were net sellers of 4,000 soybean contracts and were net even in wheat, they said.