Bank America, Corp. reported a 26 percent increase in net income and in consolidated income before securities transactions for the first quarter of 1979.

The firm, parent corporation of giant Bank of America, said income jumped to $129.2 million for the first quarter from $102.5 million one year ago.

Corporation president A. W. Clausen credited most of the increase to Bank America's continued growth in earnings assets, as well as to improvement in the net interest margin.

Bank America's assets totaled $91.3 billion at the end of the first quarter, compared with $81.6 billion at the same time last year, an increase of 11.9 percent. Total deposits were $71.3 billion, up 8.1 percent from $65.9 billion.

American Express Co. reported record first quarter earnings for the period ended March 31, with net income rising 16.1 percent from the same quarter in 1978.

Earnings for the quarter were $73.3 million ($1.02 per share) up from the previous year's $65.4 million (91 cents). Revenues for the period were $1.07 billion, a gain of 16.7 percent from $916.9 million in 1978.

Each of the company's three major lines of business reported gains in earnings for the quarter. Travel services rose 8.1 percent to $30.9 million, insurance services gained 13 percent to $40 million and international banking services were up 20 percent to $88 million.

The firm reported that the American Express Card continued to achieve new records in charge volume and membership in the first quarter.