The Carter administration announced yesterday a plan to shore up farm prices by reducing U.S. wheat production 20 per cent next year.

At the same time the administration said it will create a strategic grain reserve of 30 million to 35 million metric tons, for use when harvests fail and prices rise.

Announcing President Carteer's decision on the sensitive issue at the White House, Deputy Agriculture Secretary John White and other Agriculture Department officials said the production cutback should not result in an appreciate increase in domestic food prices.

The acreage set-aside, as it is called - the first time since 1973 the government will have acted to discourage full production - is designed to reduce the United States' rising wheat surplus, and thus keep the price of wheat from continuing to fall.

The decision also indicated that President Carter intends to sign the 1977 farm bill, to which he once objected, and which is near final action in Congress. The bill would extend the President's authority to take many of the steps he announced yesterday.

Yesterday's announcement climaxed an internal administration battle that pitted the Agriculture Department, speaking for American farmers, against Carter's economic and international policy advisers.

Agriculture Secretary Bob Bergland initially recommended a reduction in wheat production of at least 25 per cent. Bergland was set to announce tha President's decision last week, but had to cancel a news conference abruptly after Carter, responding to advisers who urged caution, ordered another look at the plan.

One of those advisers, Charles Schultze, chairman of the Council of Economic Advisers, was said to have cautioned against too sharp a curtailment in wheat output because of the possibility of a new round of food scarcity and higher food prices. Wheat is the world's largest crop and surplus U.S. wheat has been the world's main source of food to combat famines since World War II.

The State Department reportedly was also concerned about the need for adequate food supplies to serve U.S. diplomacy.

By settling for a 20 per cent production cutback, Carter softened the potential impact of Bergland's recommendation while still giving farmers part of the support they sought. And bylinking the cutback decision with an announcement of the creation of a strategic grain reserve, the President clearly hoped to dilute any criticism that the United States is abandoning its attempt to overcome world hunger.

Under the acreage set-aside program farmers will be asked to take out of production land equal to 20 per cent of the land they plant with wheat. Thus, a farmer who plants 200 acres with wheat would be asked to take 20 other acres on his farm out of any kind of production.

Agriculture Department officials said a decision will be made later on whether to impose a similar 10 per cent set-aside program fro feed grains such as corn. Indicating that this is likely, they said a 10 per cent set-aside "may be needed just to keep out stocks from climbing to exercise levels."

The set-aside program technically is voluntary, but includes extremely stron incentives for compliance. Wheat farmers who do not cut back production by 20 per cent next year will lose their eligibility for federal price supports and other Agriculture Department benefits on all their crops.

Howard York, director of agricultural economics at the Agriculture Department, estimated that a 20 per cent reduction in wheat production would cut overall U.S outuput next year from 260 million to 240 million metric tons. The wheat cutback, he said, will reduce the acreage planted with wheat from 74.4 million acreas to 63.5 million acres.

World grain supplies are now larger than at any time since 1972 because harvests in the last two years have been unusually bountful. According to Agriculture Department estimates, total world grain stock will be 200 million metric tons and U.S. stocks 80 million metric tons by the beginning of the 1978-79 growing season.

Agriculture Department officials also announced an increase in the price support level for corn from $1.75 to $2 a bushel, the same price set in the pending farm bill. The wheat price support level will remain at $2.25 a bushel.

The grain reserve plan announced yesterday will require the administration to seek congressional approval for creation of an internation emergency food reserve of up to 6 million tons that would be under direct government control. It would be used primarily to combat world hunger and nutrition problems.

The bulk of the remainder of the 30 million to 35 million metric ton reserve would be created by expanding a farmer-owned wheat and rice reserve program announced in April to include feed grains. Administration officials said a feed grain reserve of 17-to-19-million metric tons is planned. Under the program, the government pays farmers for the cost of storing surplus crops.