Consumer prices rose a modest 0.2 percent in June as weakness in the U.S. economy and foreign competition continued to hold inflation down.

The Consumer Price Index rose 3.7 percent in the last 12 months and the increase in inflation has slowed from a 4.1 percent rate in the first three months to a 3.3 percent rate from April to June, the Labor Department said.

The index also rose 0.2 percent in May.

Food costs edged up slightly after falling in May and transportation prices dropped, the Labor Department said. In addition to moderate fuel and food costs, economists attributed the inflation results to strong competition from imports, which has helped to keep the costs of domestic goods low, and slow growth in the economy.

The sluggish economy has contributed to lower wage demands, reflected in the continued high rate of unemployment, and the low rate of use of American plant and equipment, which has prevented bottlenecks and shortages from occurring in production and subsequent price hikes.

A separate government report issued yesterday suggested that economic activity in manufacturing has been on the rise in the last two months. The Commerce Department reported that new orders for factory durable goods rose 1.8 percent, following a 3.3 percent increase in May. Both months' increases reflected large orders for defense capital goods, the Commerce Department said.

Excluding defense orders, new orders increased 0.7 percent in June and 0.6 percent in May.

The White House welcomed the inflation news, saying that the CPI showed that "inflation is still well under control."

White House spokesman Larry Speakes said that "all economic indicators are still pointing to very strong third and fourth quarters." Speakes pointed to renewed consumer confidence, low inventory levels and moderately climbing personal income as indicators of a rebound in the second half of the year.

Commerce Secretary Malcolm Baldrige said that the new orders report "suggests that the goods-producing sector of the economy may be emerging from its doldrums of the past year.

"The main problem for our manufacturing industries has been the high level of the dollar," Baldrige said. "A quick resolution of our budget problems would lower interest rates and the dollar further."

If Baldrige is correct, a pickup in manufacturing activity could increase inflation somewhat down the road, economists said. Although prices of factory goods, many of which compete with imports, have been kept moderate, economists also said that the trouble spot in the price picture could be services, whose prices have continued to escalate.

Commerce Department chief economist Robert Ortner said that costs associated with medical and educational areas "are still rising pretty rapidly." For example, medical care costs rose 0.7 percent in June and 6.2 percent in the last 12 months.

"A multiplicity of factors is working in favor of continued low inflation," said Jerry Jasinowski, chief economist for the National Association of Manufacturers. "The unemployment rate has been fixed at a relatively high level for the past six months and capacity utilization is still declining with the result that slack demand has held prices down.

"Despite the recent 13 percent fall in the dollar, the exchange rate is still so overvalued that competitive pressure from import prices will hold down domestic inflation," Jasinowski continued. "For 1985 as a whole, inflation could come in at less than 4 percent."

Other areas that rose sharply were charges for electricity, up 1.3 percent, and local telephone services, up 4.6 percent. The rise in local telephone service costs largely resulted from the $1 access charge added to most local service bills in June. However, the index for interstate long-distance costs dropped 2.8 percent in June, the Labor Department said.

Fuel oil prices dropped 2.8 percent during the first half of the year and they are 15.3 percent below the peak level of April 1981.

Food and beverage costs rose 0.1 percent, the first increase in four months. Grocery store food prices dropped for the fourth consecutive month. The index for meats, poultry, fish and eggs rose for the first time since last December. During the first six months this year, beef prices have decreased 6.7 percent, Labor said. The four consecutive months of declines in fruit and vegetables prices last month have now offset sharp increases from earlier this year, Labor said.

Used-car prices dropped sharply in June and May, although gasoline prices rose a modest 0.2 percent last month. Gasoline prices have risen 7.6 percent in the past four months, but that level is still 11 percent below the peak of March 1981, the Labor Department said.

The consumer price index in June was 322.3, meaning that goods costing $10 in 1967 cost $32.23 last month. A separate consumer price index used for indexing Social Security and some other federal payments was 318.7 in June.