CANBERRA, Oct 4 (Reuters) - Chicago soybean futures rose on Wednesday as the U.S. dollar eased from 11-month highs, but prices remained near their lowest since 2021 amid signs of a better-than-expected U.S. harvest and rapid planting of crops in Brazil.

Corn prices also gained but wheat fell.

"We are seeing more soybean supply coming in and putting pressure on the market," said Andrew Whitelaw at Australian agricultural consultancy Episode 3.

Most-active Chicago Board of Trade (CBOT) soybean futures were up 0.6% at $12.80-1/4 a bushel by 0426 GMT.

Prices have fallen around 9% in the last five weeks and slipped to $12.57 on Tuesday, equalling an 18-month low seen in June.

Soybeans have been pushed lower by a stronger U.S. dollar, which makes dollar-priced beans more expensive for buyers with other currencies and can reduce demand.

The U.S. harvest is well underway, boosting supply, and government data this week showed a slight improvement in bean condition ratings.

Commodity broker StoneX raised its forecast for the average U.S. soybean yield to 50.4 bushels an acre from 50.1, estimating U.S. production at 4.175 billion bushels.

While private sales of 265,000 metric tons of U.S. soybeans to China suggested there are buyers in the market, basis values for soybeans shipped by barge to the U.S. Gulf Coast and loaded for export were steady to lower on Tuesday.

Meanwhile, a report on Monday showed farmers in Brazil, the world's biggest soybean producer, were planting new crops at the fastest pace on record.

Brazil is forecast to produce a record soybean crop this year.

Whitelaw said soybeans had been supported by a rise in oil prices that boosted ethanol, an alternative fuel made from plants including soy. But while crude remained above $90 a barrel, it has fallen $7 from last week's highs.

Commodity funds were net sellers of Chicago soybeans and corn and net buyers of wheat on Tuesday, traders said.

Chicago corn futures were up 0.1% at $4.88 a bushel on Wednesday and wheat fell 0.8% to $5.63-3/4 a bushel. Ample supply is holding prices of both crops near three-year lows.

The U.S. Department of Agriculture on Tuesday said China bought 220,000 metric tons of U.S. soft red winter wheat -- the first Chinese purchase of that class of wheat from the U.S. since July 2021.

Ukraine, a large wheat exporter, said on Tuesday it hopes to speed up exports of grain and other farm products by shifting some border checks from its busy frontier with Poland to the Lithuanian port of Klaipeda.

Two more vessels are also heading towards the Ukrainian Black Sea port of Odesa, a Ukrainian lawmaker said.

(Reporting by Peter Hobson; Editing by Krishna Chandra Eluri)