American Telephone & Telegraph Co. reported yesterday that it earned more than $6 million in 1980, with profits improving as the economy recovered from a recession.

AT&T said profits for 1980 rose 7.1 percent to $6.08 billon from $5.67 billion in 1979. Earnings per share increased 1.9 percent to $8.19 in 1980 from $8.04 a year earlier, reflecting the issuance of more stock.

No American company has ever made more money than AT&T in one year.

AT&T Chairman Charles L. Brown said 1980 was characterized at its beginning by recession and persistent inflation and in the second half of the year by an upturn in the volume of business.

"Earnings were strengthened through vigorous marketing, firm control of costs, technological innovation, rate increases and strong growth in productivity," he said.

The improvement late in the year was evident in data covering the last three months of 1980: Profits rose 13.4 percent to $1.61 billion from $1.42 billion in the same period of 1979. Earnings per share were up 7.1 percent to $2.12 from $1.98 a year earlier.

AT&T releases its earnings on the basis of quarters ending in February, May, August and November, but it also releases calendar-year figures. It previously reported earnings of $6.04 billion ($8.18 a share) in the 12 months ended Nov. 30.

Operating revenues for the year rose 11.9 percent to $50.79 billion from $45.41 billion. For the quarter, revenues were up 13 percent to $13.27 billion from $11.74 billion.

While profitability by one key measure -- return on common shareholders' equity -- slipped to 12.69 percent in 1980 from 12.94 percent in 1979, return on total capital, including borrowed funds, rose to 9.91 percent from 9.81 percent.

Pan American World Airways Inc. lost $60.4 million from its airline operations in the final quarter of 1980 and had an operating deficit of $129.6 million for the full year, the company announced yesterday.

The losses are the largest among the U.S. airlines that have reported their final 1980 results.

Pan Am's losses compared with an operating profit in 1979's fourth quarter of $28.8 million and an operating loss of $37.8 million for all of 1979.

William T. Seawell, Pan Am's chairman and chief executive officer, attributed the airline's deficits to "the poor economic climate and resulting traffic decline" and to sharp increases in its fuel and labor costs.

Pan Am managed to report a net gain for the year of $80.3 million because of a $294.4 million gain from the sale of its Grand Central Building Inc. subsidiary in New York.

For the full year, Pan Am had operating revenues of $3.55 billion, up 12 percent from $2.48 billion in 1979.

The company's net income for the fourth quarter was affected by a $11.4 million provision for employe severance costs, $7 million for losses connected with retiring the airline's remaining Boeing 707 aircraft and $3.4 million for losses on investments in Afghanistan and other countries.

Gannett Co., one of the country's largest communications combines had its 53rd consecutive year of profit gains in 1980.

Net income for the year was $151.98 million ($2.81 a share) on revenues of $1.215 billion, up from $134.08 million ($2.50) in 1979 on revenues of $1.065 billion. The revenue gain was 14 percent.

Fourth-quarter net income was $47.87 million (88 cents) on revenues of $336.7 million compared with $41.56 million (77 cents) a year earlier on sales of $295.79 million.