In a move to prop up the staggering farm economy by pushing up prices, the Reagan administration yesterday urged farmers to reduce their 1982 planting of wheat, feed grains, cotton and rice by 10 to 15 percent.

The aim of the program, announced in Kansas City by Agriculture Secretary John R. Block, is to increase farm prices by reducing the supply of basic commodities, which have just come through another bumper harvest.

Inflation and high interest rates, a strengthened dollar that has weakened export demand, falling prices, record crops of wheat and corn and near-record crops in other commodities have combined to put net farm income to its lowest level since the Depression year of 1933.

That combination of factors, with the prospect of a worsening situation this year, put the administration under heavy pressure from farm organizations and members of Congress to reestablish an acreage-reduction program similar to those of the 1960s and 1970s. The last of these was for the 1978-1979 wheat crop.

Block acknowledged that a production control program, even on a voluntary basis, runs counter to the administration's "free market" farm policy, but he said, "I have greater philosophical problems with low farm prices."

"I would prefer to not be in the position of announcing an acreage-reduction program," Block said, "but prices are unacceptable and one of the means to correct this is to work toward reducing supply."

More high-level production and low prices this year also would raise the potential for higher federal budget expense. The 1981 bumper crop cost the treasury about $1 billion in unanticipated direct subsidy payments to farmers.

Although Block and other Department of Agriculture officials described the acreage-reduction as "voluntary," there are several catches. Participants must devote set-aside land to conservation; farmers who do not participate will not be eligible for price-support loans or the direct subsidies, known as deficiency payments.

Commodity organizations and legislators had urged Block to provide direct payments to promote participation in the acreage reduction. Otherwise, they argued, farmers would plant as much land as possible and forgo government price protection.

But Block said he believed that a voluntary program, "a self-help effort for all of agriculture," would have sufficient impact on 1982 production to raise the price of wheat and corn by as much as 20 cents a bushel. He said that increases of this size "would not have any noticeable effect on consumer prices."

With record crops just harvested, wheat and corn prices have plummeted. According to the USDA, the bushel of wheat that sells for an average of $3.69 this month brought $4.21 a year ago. Corn that sold for $3.19 last January is averaging $2.40 this month.

The department reported yesterday that farm prices this month showed their first increase in 13 months, moving up 1.6 percent over December. But they still were averaging 9.7 percent less than a year ago. Last year was the first year since 1933 that farm prices failed to rise during any one of the 12 months.

The USDA also said, however, that farmers' expenses were up by 2 percent for the month and 4.1 percent above January, 1981, levels.

The program outlined by Block yesterday seeks a 15 percent reduction in acreage of wheat, rice and cotton and at least a 10 percent cut in corn and feed grains (barley, oats and sorghum).

With about 75 percent of the new wheat crop already planted, Block said that acreage designated for reduction could be cut for hay or grazed so that it would not be lost.

Before he flew to Kansas City yesterday, Block asked for and received House Appropriations agriculture subcommittee approval of an emergency $5 billion for the Commodity Credit Corp. to keep farm-program financing alive. Full commottee action is expected this week.