SINGAPORE/PARIS- Chicago wheat futures edged higher on Wednesday, hitting a new near one-week high on global supply concerns fuelled by a sharp downward revision of Canadian crop estimates at a time of strong global demand.

Corn rose for a second session, while soybeans bounced back.

"Wheat futures are down but tightness in supplies is supportive in the physical market," said Ole Houe, director of advisory services at brokerage IKON Commodities in Sydney.

The most-active wheat contract on the Chicago Board of Trade (CBOT) gained 0.5% to $7.04-1/4 a bushel by 1212 GMT after hitting a Sept. 9 high of $7.05-3/4 earlier in the session. They had closed 2% higher on Tuesday.

Soybeans Sv1 were up 0.55% at $12.89-1/2 a bushel and corn added 1.1% to $5.50 a bushel.

Canada's drought conditions damaged the wheat harvest even more than it appeared weeks ago, according to a Statistics Canada report estimating spring wheat output at 15.3 million tonnes, down 41% year on year. 

"Canada’s spring wheat crop is likely to be even worse than feared," Commerzbank said in a note. "At the same time, numerous import countries have been submitting international tenders for wheat in recent days, which is being interpreted as a sign of robust demand."

In France, farm office FranceAgriMer lowered its forecast of soft wheat exports outside the European Union in the 2021/22 season taking account of a lower estimate of this year's harvest and citing high freight costs that favour intra-EU sales. 

A fall of the dollar and strong crude oil prices were also supportive, notably for corn, the main ingredient to make ethanol in the United States.

Commodity funds were net buyers of CBOT corn, wheat and soyoil futures contracts on Tuesday and net sellers of CBOT soybeans and soymeal, traders said. 

(Reporting by Naveen Thukral; editing by Uttaresh.V and Alexander Smith) ((naveen.thukral@thomsonreuters.com; +65-6870-3829; Reuters Messaging: naveen.thukral.thomsonreuters.com@reuters.net))