* Run of importer demand helps counter harvest pressure in wheat

* Corn, soybeans edge away from 2020 lows as weather watched

* Soybeans end mixed as firm cash markets lift nearby futures

CHICAGO, July 17 (Reuters) - U.S. wheat futures rose 1.6% on Wednesday on bargain buying one day after a drop in prices to four-month lows appeared to spur fresh export business, traders said.

Corn futures ended firm while soybeans were mixed, but both markets hovered near their lowest levels in nearly four years.

Benchmark wheat futures on the Chicago Board of Trade settled up 8-1/2 cents at $5.39-1/4 per bushel, a day after falling to $5.25-1/4, the lowest on a continuous chart of the most-active contract since March 11.

CBOT corn ended up 3 cents at $4.11-3/4 a bushel. For soybeans, the nearby August contract rose 6-3/4 cents to finish at $10.97-1/4 a bushel while most-active November fell 2-1/4 cents at $10.41.

Wheat's rebound reflected a flurry of global export deals. Algeria's state grains agency bought about 600,000 metric tons of milling wheat in an international tender, European traders said. And Egypt's state buyer booked 770,000 metric tons of mostly Russian wheat on Tuesday, its biggest single purchase since 2022.

Asian wheat buyers, meanwhile, have stepped up purchases in recent weeks, taking cargoes from the Black Sea region.

"End users see some value at these price levels," StoneX chief commodities economist Arlan Suderman said in a client note.

A decline in the dollar lent support to CBOT futures, in theory making U.S. grains more competitive globally. The dollar eased as top Federal Reserve officials indicated they were getting closer to cutting interest rates.

CBOT corn inched higher but generally favorable crop weather in the Midwest hung over the market, capping rallies by bolstering expectations for large U.S. harvests. The corn crop is in the midst of pollination, its key reproductive phase.

"The month of July as a whole is expected to end up wetter than normal across most of the Corn Belt ... which will be quite favorable for development of corn and soybeans," satellite technology company Maxar said in a note.

Midwest farmers are still assessing crop damage from severe storms and strong winds that raked the region on Monday, Maxar noted.

While the weather outlook pressured new-crop November soybean futures, the nearby August contract rose for a second session on firm cash markets. U.S. farmers have been reluctant sellers of what remains of their 2023 harvest, supporting cash bids for soybeans at a time when improved crush margins have spurred demand from soy processors, traders said. (Reporting by Julie Ingwersen in Chicago Additional reporting by Gus Trompiz in Paris and Naveen Thukral in Singapore Editing by Matthew Lewis and Sandra Maler)