* Corn touches 3-week high, soybeans near 5-week peak
* Demand optimism after weekend trade deal supportive
* Rainy Midwest weather seen delaying U.S. harvests (Recasts throughout with corn and soybeans rebounding, adds quote, updates prices, changes byline, changes dateline from HAMBURG)
By Karl Plume
CHICAGO, Oct 2 (Reuters) - U.S. corn and soybean futures firmed for a second day on Tuesday on expectations for improved demand following a recent price slump and as a rainy weather outlook for the Midwest threatened to stall harvesting.
Futures jumped sharply on Monday on news of a newly negotiated U.S.-Mexico-Canada Agreement (USMCA), a replacement for the North American Free Trade Agreement, offsetting pressure from big supplies and forecasts for a bumper harvest.
"I think grain demand bulls are taking positions here, given the new USMCA, and given rain delays for row-crop harvests," said Mike Zuzolo, president of Global Commodity Analytics.
The U.S. Department of Agriculture said the corn and soybean harvests remained ahead of the normal pace as of Sunday, at 26 and 23 percent complete, but rain in key production areas of the Midwest is poised to stall harvest progress.
"The 11- to 20-day outlook has been kicking up more rainfall totals and some concerns about flooding in the western Corn Belt," Zuzolo said.
Chicago Board of Trade December corn was 3/4 cent higher at $3.66-1/2 per bushel as of 11:37 a.m. CDT (1637 GMT) after earlier touching a three-week high. November soybeans gained 4-1/2 cents to $8.62-1/4 a bushel.
Gains in both markets remain capped by ample supplies, both in the United States and globally.
INTL FCStone on Monday raised its estimate of the average U.S. 2018 corn yield to 182.7 bushels per acre (bpa), from 177.7 bpa in August. The brokerage raised its forecast of the U.S. 2018 soybean yield to 54.0 bpa, up from 53.8 bpa.
Brazil's 2018-19 soybean crop is seen reaching a record 120.4 million tonnes, a Reuters poll found.
The USDA on Friday reported higher-than-expected quarterly stocks of U.S. grains and soybeans.
Wheat futures eased on concerns about slumping demand for U.S. wheat amid stiff global competition from major exporters such as Russia.
Still, Taiwan bought 110,000 tonnes of U.S. milling wheat in an international tender on Tuesday.
CBOT December wheat shed a penny to $5.08-1/2 a bushel. (Additional reporting by Michael Hogan in Hamburg and Naveen Thukral in Singapore, editing by Alexander Smith and Tom Brown)