Inflation continued at its new, slower pace in May as consumer prices rose at a 10.9 percent annual rate, well below that of the first three months of the year, the government reported yesterday.

The May increase of 0.9 percent was the same as that in April. In each of the first three months of the year, prices rose 1.4 percent.

Consumer prices in the Washington metropolitan area also slowed in the April-May period, rising 1 percent in the two months combined. Supermarket prices here actually fell 0.5 percent during the period.

The combination of figure prompted new optimism by the Carter administration. White House inflation adviser Alfred E. Kahn told Congress that inflation would slow to a 7 to 8 percent annual rate by July.

But government and private economists cautioned that the relief would probably be only temporary, and that inflation most likely would persist at a 10 percent annual rate late this year and early in 1981.

The Agriculture Department predicted yesterday that food prices will rise at an annual rate of between 11 and 12 percent in the third quarter, compared to 9.5 percent this quarter, as meat prices begin to climb.

Kahn, however, said that for the short run, at least, Americans will be getting a break as a pause in soaring energy prices and a decline in mortgage interest rates help hold the price index in check.

It was the sharp increase in these items earlier this year that pushed inflation up to its 18.1 percent annual rate during January, February and March. Economists complained then that the index was "distorted" upward.

Kahn told Congress yesterday that the same forces that skewed the index too high last winter were pushing it down this summer. "We are now getting something which is more nearly indicative of the underlying inflation rate," he said.

Unlike the earlier months of the year, wages kept pace with prices in May. Average hourly earnings, adjusted for inflation, remained unchanged.

Over the last year, however, the impact of inflation on American's pocketbooks has been substantial. The Labor Department reported yesterday that "real" earnings have declined 4.7 percent in the last 12 months.

The continued moderation on the inflation front came without much help from the recent decline in mortgage interest rates. Because of normal lags in data-collection, the declines won't show up until June or July.

Yesterday's report showed food prices nationally up 0.3 percent in May following an 0.5 percent rise the previous month. But contrast, food prices rose 1 percent in March after remaining stable earlier this year.

Energy prices rose 0.8 percent in May, following an 0.9 percent rise in April, as last year's hefty rise in oil prices worked its way through the economy. The increase in March had been a staggering 3 percent.

And housing costs rose 1.5 percent in May, showing a continued upward surge because of delays in collecting the data. The housing index rose 1.3 percent in April, following increases of 1.4 to 1.6 percent from January through March.

There also were substantial improvements in other major categories of goods and services, partly reflecting the dropoff in consumer demand in the face of the deepening recession.

Prices of apparel and upkeep, for example, declined 0.2 percent in May after rising 0.3 percent the previous month. By comparison, in March, these prices soared a full 2 percent.

Prices of new cars shot up 1.1 percent in May, on the heels of a 1.6 percent increase in April -- all this in the face of sharply declining sales and offers of rebates by the major manufacturers.

The overall consumer price index stood at 244.9 percent of its 1967 average, up 14.4 percent from a year ago. That means it took $244.90 to buy the same goods and service at retail in May that cost $100 just 13 year ago.

Kahn told the congressional joint Economic Committee yesterday that the continued decline in home mortgage interest rates "will almost certainly take the consumer price index below 10 percent . . . many points below . . . in July."

Later, he told reporters that the index would be rising at a 7 to 8 percent annual rate in another couple of months. Administration officials earlier had forecast such a break, but were dismissed as too optimistic.