President Reagan said yesterday that the government will give 30 million pounds of surplus processed cheese to needy American families.

The decision, which the president announced as he signed a new four-year farm bill, was in response to growing political pressure to dispose of some of the surplus dairy products the government has acquired under its costly milk price support program.

The government holdings have been steadily growing -- they now amount to more than 560 million pounds of cheese -- and the president said that "at a time when American families are under increasing financial pressure, their government cannot sit by and watch millions of pounds of food turn to waste."

The cheese, valued at $43 million, will be made available to states that request it and to private charitable organizations approved by the Department of Agriculture to distribute the surplus to needy families, which will include food stamp recipients. A state, therefore, may have more than one distribution program.

Yesterday's action, according to USDA officials, could be a prelude to the distribution of more cheese stocks in the near future. Supplies are accumulating rapidly and prospects are not considered bright for selling them.

Californians apparently will be the first to receive the gift cheese. A state proposal for distribution of surplus already has been approved and Merritt Sprague, a USDA commodity-distribution official, said the first "token" transfers could occur before Christmas.

One problem with the cheese now in storage is spoilage. Warehouses in 35 states hold 221 million pounds of processed cheese in five-pound bricks, and 339 million pounds of natural cheddar cheese in barrels and blocks.

Congressional offices, the USDA and the White House have been bombarded with requests for free cheese and suggestions for its distribution since disclosure several weeks ago that the government was weighing options for disposing of some of the surplus.

Ironically, the farm bill Reagan signed yesterday will do little to stem the flow of surplus milk products into government hands. The new law will hold dairy price supports at current levels, but will cost taxpayers an estimated $2 billion anyway during this fiscal year to buy surplus cheese, butter and nonfat dry milk.

The soaring cost of the dairy program was one of the first targets of the administration's budget cutters. The president won a crucial test last spring, preventing a scheduled April 1 increase in support levels, but the dairy issue ignited a fiery debate on Capitol Hill.

The new law gave the administration less than it sought in holding down dairy program costs. It will allow higher price supports if farmers are able to reduce their milk production over the four-year life of the statute.

As Reagan met with congressional agriculture leaders for the White House bill signing ceremony, a new USDA economic projection said that American dairy cows will have another record year in 1982 -- up from 1 to 3 percent over this year's historic high of about 132.3 billion pounds.

Officials of the Commodity Credit Corp. (CCC), the arm of USDA that handles dairy and other commodity surpluses, calculate that this continued high level of production will result in the acquisition of at least 300 million more pounds of excess cheese this fiscal year.