* Market awaits U.S. grains stocks, inflation data

* Grains set for quarterly fall as Brazil, Russia supplies weigh

PARIS/SINGAPORE, Sept 29 (Reuters) - Chicago corn, wheat and soybeans edged up on Friday, with corn setting a new multi-week high, as market participants adjusted positions before closely watched U.S. grain stocks figures later in the day.

Friday's release of U.S. price data, a pointer towards interest rate policy, and the threat of a partial U.S. government shutdown from this weekend were adding to uncertainty on the last trading day of the month and the quarter, analysts said.

The most-active corn contract on the Chicago Board of Trade (CBOT) was up 0.1% at $4.89 a bushel by 0916 GMT. It earlier touched its highest since Sept. 6.

CBOT wheat was up 0.7% at $5.82-1/2 a bushel while soybeans added 0.3% to $13.04-1/4 a bushel.

A pullback in the dollar index after a 10-month high this week lent some support to U.S. commodities.

Corn has attracted short-covering by investors holding a large net short position in the cereal, according to analysts.

Chicago corn, wheat and soybeans are currently set for a quarterly fall, extending a broad decline this year as hefty supplies of corn and soybeans in Brazil and wheat in Russia have tempered concerns about war in Ukraine and drought in some exporting countries.

Friday's USDA stocks report is closely watched as a gauge of U.S. supply as farmers start to bring in the corn and soybean harvests. The USDA will also issue an updated estimate of U.S. wheat production.

Before that, financial markets will be assessing the U.S. personal consumption expenditures price index.

"Important U.S. macroeconomic data, followed by USDA reports, will set the tone," brokerage Copenhagen Merchants said in a note.

Grain prices remained curbed by exports flowing from Brazil and the Black Sea region.

Black Sea supply worries have eased with the resumption of Ukraine's exports through a shipping channel.

Chinese importers are believed to have made large purchases of animal feed corn from Ukraine in the past two weeks, traders said on Thursday.

However, dry weather in Argentina and Australia was still a concern for wheat supply this season.

"We don't see a downside in prices from the current levels. In fact, prices are likely to rise as dry weather in Australia, Canada and Argentina is reducing output," one Singapore-based trader said of wheat.

(Reporting by Gus Trompiz in Paris and Naveen Thukral in Singapore; Editing by Rashmi Aich, Sherry Jacob-Phillips, Elaine Hardcastle)