A surge in auto imports from Japan following the end of voluntary restraints helped widen the U.S. trade deficit in April by $11.85 billion, the Commerce Department reported yesterday.

"The rise in imports of automobiles was largely from Japan, marking the beginning of a new fiscal year and the end of the voluntary restraint program," said Commerce Secretary Malcolm Baldrige. "Imports of Japanese automobiles surged to $1.4 billion from $1.0 billion in March and an average of $1.1 billion per month during 1984."

The $11.85 billion increase in the deficit was the third-largest monthly increase in history. If the trade deficit continued to grow at the pace set in the first four months, at the end of the year it would be a record $133.9 billion.

In addition to the increase in Japanese auto imports, a large surge in oil imports also helped the trade deficit widen from $11.05 billion in March.

Separately, the Commerce Department reported that factory orders declined in April for the third consecutive month, suggesting that the economic slump will continue into the second half of the year. Orders for new factory goods in April dropped 0.5 percent following a 0.7 percent decline in March and a 1.1 percent fall in February.

The fall in factory orders and subsequent decline in many manufacturing industries reflected the increasing trade problems brought about by the high value of the dollar, economists said. The dollar's value makes foreign goods relatively less expensive than domestic products, and businesses and consumers have been taking ample advantage of that price difference.

Both the new orders and trade deficits reports "were weaker than expected and point to a significant slump in economic activity in the second half of this year," said economist David Jones of Aubrey G. Lanston.

Jones said that economists earlier expected an improvement in economic growth during the second quarter of 1985 following a 0.7 percent increase in real gross national product during the first three months of the year.

However, the sluggishness probably will continue through the third quarter, too, Jones said. The new-orders figures tend to be forward looking in that they reflect orders for equipment to be used about three months in the future. "The decline in factory orders is consistent with the view that we will have a softer economy," Jones said.

Particularly alarming in the April report on new orders was the second consecutive monthly decline in new orders for nondefense capital goods. In addition, the backlog of new orders fell in April for the fifth time in the last eight months, Jones said.

In addition, the April decline in new orders for durable goods, resulting in large part from substantial declines in the machinery industries, continues to be of concern, Jones said.

On the trade side, the Commerce Department reported that U.S. exports fell 3.6 percent in April while imports rose 0.5 percent. Oil imports increased 49.7 percent. For the first four months of the year, the trade deficit was $44.63 billion, compared with $42.02 billion during the same period last year.

Agricultural exports, which for years had been among the most consistently strong performers, increased 2.2 percent in April, but remained below their first-quarter average, Commerce said.

"The trade-weighted value of the dollar reached a peak in late February and has since fallen about 7 percent," Baldrige said. "The dollar's decline so far is not enough to improve U.S. competitiveness and should have only a limited effect on our balance of trade."

The removal of voluntary trade limits against Japan in April was greeted with warnings that Japanese automobiles would flood U.S. markets and create problems for domestic manufacturers. Japan said that it would limit its annual auto shipments to the United States to 2.3 million units, more than a 25 percent increase over the 1.85 million vehicles exported here in 1984.

In April, passenger cars from Japan numbered 176,863, a 29.4 percent increase over April 1984. However, Commerce officials noted that the monthly numbers tend to jump around.

Under last year's voluntary agreement, cars from Japan averaged 150,000 a month. According to this year's plan, that average would increase to 190,000 a month, slightly above the number of cars imported this April.

The trade deficit with Japan was $4.0 billion for April, compared with $3.2 billion for March, Commerce said.

April imports reflected the "net effect of increases in petroleum products and declines in manufactured goods and agricultural commodities," the Commerce Department said. The increase in petroleum products was primarily the result of a large number of March crude petroleum shipments being included in the data for April because of the late receipt of various import documents, the department reported.

Imports of clothing, general industrial machinery, and iron and steel mill products declined.

The trade deficits with Canada narrowed from $2.067 billion for March to $2.054 billion for April; with Western Europe from $1.68 billion for March to $1.66 billion, and with Taiwan from $1.3 billion for March to $1.1 billion.