* Australia cuts wheat output forecast on dry El Nino weather

* Black Sea supplies still curbing wheat prices

* Corn, soy markets assess weather before weekly crop ratings

PARIS/SINGAPORE, Sept 5 (Reuters) - Chicago wheat futures edged higher on Tuesday, steadying after a new three-month low as the market set competition from Black Sea supplies against dry weather threatening production in other export hubs like Australia.

Corn was almost unchanged while soybeans ticked lower as participants assessed weather forecasts for the U.S. Midwest and awaited weekly government crop ratings to gauge the impact of a hot spell.

A firm dollar, reflecting renewed investor concerns about economic growth, helped cap U.S. grain prices.

Chicago futures were resuming trading after Monday's closure for the U.S. Labor Day holiday.

The most-active wheat contract on the Chicago Board of Trade (CBOT) was up 0.6% at $5.99-1/4 a bushel at 1110 GMT, after slipping to its lowest since June 1 earlier in the session.

Wheat struck three-month lows last week as bumper Russian supply and continuing Ukrainian exports, despite the collapse of a wartime Black Sea grain deal, hung over the market.

However, dry conditions in major exporters Australia, Argentina and Canada have raised doubt about availability later in the season.

"Wheat markets still appear relatively relaxed despite the fact that the signs of tightening supply are gradually increasing," Commerzbank analysts said in a note.

Australia's wheat output is forecast to drop by 36% from last year as dry weather curbs yields, the Australian Bureau of Agricultural and Resource Economics and Sciences said on Tuesday as it trimmed its outlook by 800,000 metric tons from previously to 25.4 million tons.

"If it remains dry in September, we are looking at further downgrades in Australia's wheat crop," a Singapore-based trader said.

In Argentina, though, recent rainfall has brought relief to the wheat crop, the Rosario grains exchange (BCR) said Monday.

Egypt's state grains buyer bought about half a million metric tons of Russian wheat in a private deal, four traders told Reuters.

Record Russian exports in the past year have eased worries about disruption due to Moscow's war with fellow grain exporter Ukraine.

Turkish President Tayyip Erdogan said after talks with Russia's Vladimir Putin on Monday that it would soon be possible to revive the grain deal allowing Ukrainian shipments from Black Sea ports, though Putin repeated Moscow's position that its demands regarding Russian exports would need to be fulfilled.

CBOT corn inched down 0.1% to $4.81 a bushel and soybeans eased 0.4% to $13.63-1/4 a bushel.

A hot, dry end to summer has caused concern about further stress to U.S. corn and soybeans, though traders see limited risks with the harvest approaching and cooler temperatures plus showers expected in the week ahead.

Soybeans were pressured by weakness in related vegetable oil markets.

(Reporting by Gus Trompiz in Paris and Naveen Thukral in Singapore; Editing by Sherry Jacob-Phillips, Sohini Goswami and Ed Osmond)