The government's index of leading indicators, a guide to future movement in the economy, dropped 1.8 percent in May after a 0.4 percent rise in April, the Commerce Department reported yesterday.

The May drop -- the largest since May 1980 -- adds to evidence that the economy slowed down in the April to June quarter, after rapid growth in the first three months of the year.

Commerce Secretary Malcolm Baldrige commented that "the decline in the index of leading indicators for May, together with other information available, suggests that the economic recovery that began last summer temporarily has stalled." He used the occasion to call for swift enactment of President Reagan's economic program of tax and spending cuts.

"Since the end of last year the leading index has been telegraphing the message of a slowdown," he said. "Something is needed to give a 'boost' to the economy at this point. Enactment of the president's economic program should provide that boost, setting the stage for a pickup in activity later this year and a healthy expansion thereafter."

Meanwhile, a separate report from the Commerce Department showed that new factory orders rose by 0.6 percent in May, to a seasonally adjusted $164.93 billion. This compared with a rise of 0.5 percent in April.

Durable goods orders fell 0.2 percent during May, the report said, to $84 billion, while new orders for nondurables rose by 1.4 percent to $80.8 billion.

High interest rates during the latest quarter have probably contributed to a downturn in the economy, experts say. Both private and government economists have been expecting growth to slacken over the summer and to remain flat for the rest of the year.

The administration does not predict recession, Baldrige said, although the economy "appears to have shown no significant change between the first and second quarters."

The May decline in the index was the third recorded this year. In January and February the leading indicators declined, but this was reversed in March and April largely because of rising crude oil prices.

The prices of raw materials for industry, which are considered sensitive to changes in demand, are one element in the leading index. A rise in these prices is thought to reflect strength in the economy.

A change in these prices was the biggest contributor to the May decline in the index, the Commerce Department said. All but one of the 10 leading indicators recorded in May pushed the index down, the report showed.

These included the layoff rate, new orders, vendor performance, contracts and inflation-adjusted orders for plants and equipment, building permits, stock prices, and money supply and total liquid assets. The average work week increased against the trend.

The leading index now stands at 135.2 percent of its 1967 base.