CANBERRA, April 2 (Reuters) - Chicago wheat futures fell on Tuesday amid expectations of strong supply from Russia and data showing good crop conditions in the United States, while a rising dollar added pressure by making U.S. farm exports costlier for importers.

Soybean and corn futures inched higher.

FUNDAMENTALS

* The most-active wheat contract on the Chicago Board of Trade (CBOT) was down 0.1% at $5.56-1/4 a bushel by 0034 GMT, while CBOT soybeans had risen 0.1% to $11.86-3/4 a bushel and corn climbed 0.1% to $4.36 a bushel.

* All three contracts were close to their lowest levels since 2020 due to plentiful supply, and speculators have built up large net short positions.

* The U.S. Department of Agriculture (USDA) in its first weekly crop progress report of the 2024 growing season rated 56% of the U.S. winter wheat crop in good-to-excellent condition, below an average of trade expectations but still the highest for this time of the year since 2019.

* Last week, the USDA said U.S. wheat stocks had risen more than expected, while reporting higher soybean and corn stocks and a likely fall in corn planting.

* Russian wheat export prices rose for the third week in a row last week, analysts said, and the country was estimated to have exported 4.9 million metric tons in March, the most for any March on record.

* The U.S. dollar on Monday reached its highest level against a basket of major currencies since mid-November.

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

* Ukraine's grain exports fell to around 5.2 million metric tons in March from 5.8 million tons in February, something blamed upon Russian shelling interrupting operations at seaports, and Polish protesters blocking of land exports.

* Brazil's soybean harvest for the 2023/24 cycle had reached 74% of the planted area as of last Thursday, consultants AgRural said on Monday.

MARKETS NEWS

* Gold prices hit fresh all-time peaks on Monday with stocks on Wall Street closing mixed as optimism that the Federal Reserve was near to cutting interest rates faded due to a strong U.S. economy that rebuts the need for cuts anytime soon.

(Reporting by Peter Hobson; Editing by Subhranshu Sahu)