A drop in exports coupled with a sharp rise in automobile imports widened the United States' trade deficit last month, the Commerce Department reported yesterday.

The deficit on merchandise trade rose to $1.64 billion, after seasonal adjustment, from $1.06 billion in August, the department reported.

U.S. exports fell by 2.1 percent in September to a seasonally adjusted $18.7 billion. They had risen by a healthy 5.7 percent in August, helping to trim the trade deficit for that month to its lowest monthly total for four years.

Despite worsening in September, the U.S. trade balance is still running at a lower level than last year. For the first nine months of 1980, U.S. trade was $25.97 billion in the red compared with a gap of $27.04 billion fokr the same months in 1979.

The Commerce Department said it expects this years' trade deficit to be about $3 billion less than last year's total of $37.29 billion, itself an improvement on the record 1978 deficit of $39.56 billion.

The figure reported yesterday show imports measured inclusive of the cost of insurance and freight. This makes the deficit look larger.

The value of imported autos went up by 23.6 percent last month to $1.4 billion.

The administration has been encouraged so far this year by relatively good trade figures, as oil imports have not risen in value as much as was expected. The Commerce Department reported yesterday that the United States imported 38 percent less oil in volume terms in the first nine months of this year than in the same period in 1979. The value was down by 2.6 percent. A large part of the drop in oil consumption was due to the recession.

Exports have had a mixed performance this year. In June U.S. sales overseas jumped by 5.5 percent. They then fell 3 percent in July, before rising again in August and dropping last month.

Whereas the August increase in exports was spread across industries, the September decline was especially marked by a 2.6 percent drop in soybean exports, a 23 percent fall in shipments of nonferrous metals and a decline of nearly 13 percent in exported chemicals.

Total imports rose by 0.9 percent last month to a seasonally adjusted $20.35 billion. This followed a rise of 1.2 percent in August and a drop of 4.8 percent in July.

The value of oil imports dropped by 6.9 percent last month to $5.75 billion, while the volume of imported oil and related products fell by 5.5 percent to 176 million barrels in the month.

The trade gap with Japan widened from $985.3 million in August to $1.16 billion last month, while the U.S. surplus with Western Europe narrowed to $1.13 billion in September from $1.76 billion in August.

A separate government report issued yesterday by the Bureau of Labor Statistics showed a slight fall last month in the working time lost through strikes. In September 0.16 percent of estimated total working time (or 1.6 days per thousand) was lost because of strikes compared with 0.17 percent in August.