WASHINGTON (AP) _ The American appetite for cheese, ice cream, milk and other dairy products continues to grow, the privately supported National Dairy Board said Monday, citing a 5.7 percent rise in cheese consumption alone.

Ice cream consumption was up 2.5 percent during the board's fiscal year, which ended April 30, and milk use rose nearly 1 percent, the board said in its annual report.

Since the board was established in 1984, dairy product sales have risen nearly 10 percent, the biggest three-year gain in the industry's history, said Joseph J. Westwater, chief excutive officer.

''The investment of American dairy farmers, the work of the dairy board and other dairy promotion groups is paying off handsomely,'' he said.

A national program of promotion, research and nutrition education is financed by a mandatory assessment of 15 cents per 100 pounds on all milk produced and sold in the contiguous 48 states.

The 36-member policy-making board is composed of dairy producers.

In its report, the board said its expenditures last year totaled $79.8 million, of which $60.3 million went to advertising.