CANBERRA, Aug 2 (Reuters) - Chicago corn and soybean futures rose on Friday but were still near four-year lows and headed for weekly losses as forecasts for cool, rainy weather in the U.S. corn belt improved the supply outlook.

Wheat futures also gained and were set for a weekly gain as traders weighed the production impact of adverse weather in Europe and China, but prices remain close to four-year lows.

The most-active soybean contract on the Chicago Board of Trade (CBOT) was up 0.4% at $10.21 a bushel, as of 0448 GMT. The contract has lost 2.7% for the week, having hit $10.13 on Thursday, its lowest since 2020.

CBOT corn rose 0.4% to $4.00-1/4 a bushel, but was down 2.4% from last Friday's close, having fallen to $3.95 on Thursday, also the lowest since 2020.

"U.S. conditions are excellent so it's hard to justify high prices," Commonwealth Bank analyst Dennis Voznesenski said.

"Prospects for U.S. corn and soybeans are looking really good," he said, adding that South American harvests had already been keeping the markets well-supplied.

Dealers said U.S. farmers have begun selling corn and soy stored from the 2023 harvest as the chance of higher prices recedes and they seek to make room for the coming crop.

Commodity brokerage StoneX projected U.S. 2024 corn production at 15.207 billion bushels and soybean production at 4.483 billion bushels.

Speculators anticipating ample supplies have amassed large net short positions in CBOT soybeans, corn and wheat. Funds were net sellers of corn and soybeans and net buyers of wheat on Thursday, traders said.

CBOT wheat was up 0.5% at $5.34-1/2 a bushel and has gained 2.1% so far this week, but prices remain near a four-year low of $5.14 reached on Monday.

Storms and forecasts for more showers could halt the French wheat harvest again after farmers made progress during a hot spell early this week.

Chinese Vice Premier Liu Guozhong urged local authorities to seek to minimise agricultural losses and ensure a robust autumn grain harvest after torrential rain and floods lashed Henan, the country's largest wheat-growing province.

However, top wheat exporter Russia has maintained its official grain harvest forecast and rain in Argentina's farming heartland expected to boost wheat crops.

(Reporting by Peter Hobson; Editing by Subhranshu Sahu and Sherry Jacob-Phillips)