General Motors Corp. and Chrysler Corp. reported lower first-quarter earnings yesterday, with Chrysler taking a drop of 29.6 percent.

Chrysler posted earnings of $356.9 million ($2.36 a share), down from $507.6 million ($2.79) in the year-ago period.

But the nation's No. 3 auto maker reported record first-quarter sales of $5.8 billion, up from $5.4 billion over a year ago. The company sold 20,000 more cars and trucks in the first three months of this year than it sold during the same period of 1985.

Chrysler's earnings tumbled under the weight of heavy capital spending, higher taxes and increased labor costs, Chrysler Chairman Lee A. Iacocca said here yesterday.

GM's drop in profits was less than 1 percent, from $1.072 billion ($3.32 a share) in the year-ago quarter to $1.064 billion ($3.11) in the first quarter of 1986.

GM posted record sales of $26.8 billion during the quarter, up from a previous record of $24.2 billion in the first quarter of 1985.

But the company's income from its main business, the manufacture of cars and trucks, dropped $405 million, down from $1.5 billion in the first quarter of 1985 to $1.1 billion in the same period this year.

GM officials said the costs of sales incentive programs, new-product and plant development, and slower sales contributed to the decline in operating earnings.

*Japanese auto maker Honda Motor Co. Ltd. reported record consolidated net income of $811.4 million ($8.26 a share) for its fiscal year that ended Feb. 28, up 14 percent from levels a year ago.

Sales for the fiscal year totaled $16.1 billion, up 9.7 percent from last year. Of that, $4.6 billion, or 29 percent, came from the Japanese market, while $11.4 billion, or 71 percent, was generated from its overseas sales, including the U.S. market.

Automobile sales for the fiscal year rose 9.3 percent to almost 1.37 million units. Their sales value increased 13.7 percent to $10.2 billion, representing 63.3 percent of total consolidated sales. Motorcycle sales rose 4.2 percent to 3 million units.

For the fourth fiscal quarter, Honda's net income was $166.7 million ($1.68), down about 20 percent from a year ago. Overall sales, however, rose 6.6 percent to $4.1 billion.

*Mobil Corp., the nation's second-largest oil company after Exxon Corp., said yesterday that its first-quarter earnings rose 38 percent to $440 million.

Mobil's net income between January and March worked out to $1.08 a share, after 78 cents a share on earnings of $320 million during the same period last year.

Its revenue was $14.1 billion, down from 1985's first-quarter revenue of $15.1 billion, company officials said.

Mobil said a $39 million increase in chemical operations earnings and a combined gain of $269 million from world refining, marketing and transportation operations boosted earnings.