The U.S. economy showed signs of a continuing slowdown yesterday as President Reagan prepared to urge America's allies at the summit in Bonn to stimulate their economies to help take up the slack.

The Commerce Department reported a 0.2 percent drop in the index of leading economic indicators and a 0.9 percent decline in new orders for factory goods. Both indicators are used to gauge economic activity in coming months.

Commerce Secretary Malcolm Baldrige said the economy probably will strengthen during the current quarter, but "domestic production gains will be limited by higher imports and flat export sales. This drag on the economy would be moderated by reducing the budget deficit, lowering barriers to trade and stronger growth abroad."

In a separate report, Commerce said that the U.S. merchandise trade deficit narrowed slightly to $11 billion in March from $11.4 billion in February. The trade deficit, which is running ahead of the record 1984 pace, has been a major reason for the sharp slowdown in output. Details on Page F1.

The administration has boasted about the current economic expansion, one of the strongest since World War II, but at the Bonn summit Reagan will press leaders of West Germany and Japan to boost their economies to offset the U.S. slowdown.

The March decline in the index of leading indicators followed downward revisions in the indexes in February and January, the Commerce Department said. The index gauges economic activity between three and nine months ahead.

New orders for factory goods, also a measure of future business activity, declined 0.9 percent in March, following a 0.9 percent decrease in February. New orders now have declined in eight of the last 12 months.

The three reports, in addition to other recent statistics, describe an economy weakened by imports attracted in large part by the strong dollar, which many economists say is the result of the large federal budget deficits.

Manufacturing activity, which never fully recovered from the last recession, has been weakened as demand has shifted from domestic products to foreign goods. Figures released yesterday showing that factory inventories have increased in the last two months suggest that manufacturing weakness will continue as businesses attempt to get rid of surplus stocks.

Baldrige said the index of leading indicators is at its level of a year ago "and is likely to remain sluggish until the dollar falls." But White House spokesman Larry Speakes said that the leading indicators report should not be given much credence because the numbers often are revised after more information becomes available.

"The leading index remains well above levels registered in the second half of 1984," Speakes said. "The March decline should not be regarded with great significance since the average monthly revision is 0.4 percent."

Speakes also noted that the trade deficit narrowed slightly, but warned that "imports could go up again soon in response to the drawdown in domestic oil inventories" resulting from the expectation of lower oil prices in the future.

"The decline in the leading indicators corroborates other evidence that the economic slowdown will continue in the second quarter," said Jerry Jasinowski, chief economist for the National Association of Manufacturers. "The decline in new orders for consumer and capital goods is significant. The economy underwent a buildup in inventories during the first quarter, and these surplus stocks will have to be liquidated in the coming months."

The elimination of the inventories means that production may slow down to keep these surplus stocks under control, and as a result the employment picture probably won't improve, according to Allen Sinai, chief economist for Shearson Lehman Brothers. "All three of the reports are negatives in terms of growth in the economy," he said.

The trade deficit and the increase in inventories indicate together that growth in the second quarter may be only in the range of 2 to 3 percent, Jasinowski said.

Economic growth, which reached 4.3 percent in the final three months of 1984, slowed during the first quarter this year to a 1.3 percent pace, far below the administration's expectations.

The administration is counting on real economic growth of about 4 percent this year to prevent the federal budget deficit from growing even larger than the projected $222 billion this year and $180 billion next year.

The Commerce Department said the index of leading indicators increased 0.5 percent in February and 1.3 percent in January. Those figures were revised downward from increases of 0.7 percent and 1.5 percent.

Seven of the 10 indicators contributed to the decline in the index in March.

They were net business formation; contracts and orders for plants and equipment; manufacturers' new orders for consumer goods and materials; change in sensitive materials prices; stock prices; money supply, and vendor performance, which measures the speed at which companies receive deliveries of goods.

The positive contributors were average workweek, building permits and average weekly initial claims for state unemployment insurance.

The factory report showed orders for durable goods declined 3 percent in March, largely because of a decrease in motor vehicle and aircraft orders. Office and computing equipment orders also declined, Commerce said.

Additionally, orders for nondefense capital goods dropped 7.4 percent following a 24.8 percent increase in February. The generally volatile defense spending sector increased 22.2 percent, following a 54 percent decline in February