The price of necessities -- food, fuel, housing and medical care -- rose much faster than prices generally in the last three months, which means inflation hit hardest at the poor, a Washington-based research group reported yesterday.

Necessity prices rose at an annual rate of 17.6 percent over the quarter, while other consumer prices rose at a 6.6 percent rate.

Necessities make up a comparatively high percentage of a low-income family's expenditures. Because of that, the Consumer Price Index which measures all prices does not totally measure inflation's impact on the poor, the group said.

The new price compilation came as theAgriculture Department was predicting increases in food prices of up to 11 percent next year, along with a sharp decrease in farmers' incomes.

Noting that the price of necessities is rising more than twice as fast as the price of other goods monitored for the Consumer Price Index, the consumer-oriented National Center for Economic Alternatives said energy prices alone increased at an annual rate of more than 50 percent, while housing jumped at 17.6 percent. Food rose at a 4.2 percent rate and medical care 9.9 percent.

"Both [energy and housing] sectors are likely to experience continued severe inflation rates because of the Federal Reserve Board's tight money, high interest rate policy, and the combination of the administration decision to decontrol oil prices and OPEC's new round of increases," the NCEA report said.

For the first nine months of this year, the report notes, the price of housing jumped at an annual rate of 15.9 percent, food at 9.6 percent, medical-care costs 9 percent and energy prices 45.5 percent.

The NCEA necessities price index is reached by extracting the price increases of the four necessities from the CPI, which measures increases in many different prices.

The four categories measured by the NCEA comprise roughly two thirds of the household budget of four out of five American families, the center contends -- and the lower a family's income, the higher this fraction.

Although the new figures show that the price of necessities is increasing at a faster rate than in 1978, when they increased 10.8 percent, NCEA also reported that the present rate is a slight improvement over the second quarter of 1979, particularly in the area of food and energy.

In the three months ending in June 1979, for example, the index had increased at an annual rate of 18.6 percent, slightly higher than the third quarter's 17.6 percent jump.

But the prices of the necessities are still rising at "a frightening level," center co-director Gar Alperovitz said.

Meanwhile, in a statement to a tax conference in Washington, Treasury Secretary G. William Miller called inflation "the major domestic problem" facing the nation. He said the administration "is firmly committed to waging a vigorous battle" against it. Miller said the fight will not be won "quickly or easily," and called fiscal discipline "a major weapon in the war against inflation.'

But the liberal-leaning center was critical of the administration in the report released yesterday, claiming that the rapid phaseout of domestic crude oil price controls alone would have an inflationary impact that "will be significant [in] every quarter for the next two years, no matter what OPEC does."