* US soy harvest progress, crop conditions above expectations

* High September soy crush, falling soyoil stocks support prices

* Corn eases as harvest watched, wheat retreats from 2-week high

CHICAGO, Oct 17 (Reuters) - Chicago Board of Trade soybean futures firmed for a second straight session on Tuesday amid signs of technical trading, as strong domestic demand eased concerns about supplies growing as the U.S. harvest continued.

Corn inched down as traders monitored the U.S. harvest progress, as investors monitored Israel's war with Palestinian militant group Hamas and awaited a speech on Thursday by Federal Reserve Chair Jerome Powell.

Meanwhile, wheat eased further amid renewed pressure from large Black Sea supplies, traders said.

The CBOT's most-active soybean contract was up 1.22% at $13.02 a bushel by 1622 GMT. CBOT corn was down 0.05% to $4.89-3/4 a bushel, and wheat was down 0.48% to $5.74-1/2 a bushel.

Industry data released on Monday showed monthly U.S. soybean crush at its highest-ever level for September, and end-of-month soyoil stocks at their lowest in nearly nine years.

"That nine-year-low has this market a little bit worked up," said Karl Setzer, partner at Consus Ag Consulting.

Still, soybean futures on Tuesday were pressured by U.S. Department of Agriculture crop data released after Monday's close. U.S. farmers had harvested nearly two-thirds of their soybean crop by Sunday, above a range of analyst estimates, while soybean condition ratings also improved, the USDA's weekly data showed.

Traders also said they were keeping an eye on South America's market. While China's recent soybean buying continues to lag behind its normal seasonal pace, traders said they were also weighing whether strength in Brazil's currency could make South American supplies less competitive in the short-term.

"Buyers hope that a favorable start to Brazil's growing season will reduce the inverse in the price structure to make Brazilian beans more competitive again, which would lead them to increase purchases for December and January shipment," Arlan Suderman, chief commodities economist for StoneX, wrote in an analyst note on Tuesday.

(Reporting by Gus Trompiz in Paris and Naveen Thukral in Singaore; additional reporting by Julie Ingwersen in Chicago; Editing by Subhranshu Sahu, Will Dunham and Emelia Sithole-Matarise)