Exxon Corp., the world's biggest petroleum company, today joined the parade of major oil companies reporting sizable profit increases during 1979.

Exxon said today that its 1979 earnings rose 55 percent to $4.3 billion ($9.74 a share) from $2.76 billion ($6.20) the previous year. Sales were up 30 percent to $84.4 billion from $64.9 billion. Fourth-quarter profits rose 60 percent to $1.365 billion ($3.10) from $853 million ($1.92).

The major companies are touchy about their big profit gains in a year when American consumers have been battered by sharply rising gasoline and heating oil prices.

The petroleum companies argue -- and Exxon is no exception -- that although the earnings increases seem substantial, oil companies earn a rate of return that is not excessive among American industries and that the oil companies need the big profits to plow back into exploration for oil and natural gas.

Mobil, which reported a 78 percent profit increase, sent reporters a massive "white" paper several days before announcing its profits to explain earnings and to detail how the company spends its money. And Exxon Chairman Clifford Garvin held a rare news conference today to release the oil giant's 1979 profits. Higher profits also were reported by Sun Co., Standard Oil of Ohio and Marathon Oil.

Garvin noted that Exxon's earnings in 1979 represent 4.3 cents per gallon of products sold. Most of the company's profit increases came not from the United States, but from once-depressed foreign refining operations, especially in Europe.

About a third of the profits climb came from a lowering of taxes in Britain and a significant reduction in foreign exchange losses, the company said. "I think we've made responsible use of past profits," Garvin told reporters. "We've plowed them back into the business."

Garvin also cautioned against focusing on profits.

"American Telephone and Telegraph Co. is the only company with larger profits in dollars. But in terms of profitability (return on equity), there are hundreds of companies that are ahead of us," he asserted.

Nevertheless, by almost any measure, Exxon had a banner year. The return on shareholders' equity advanced to 20.1 percent from 14 percent in 1978 and the return on total capital employed in the business (both equity and debt) rose to 16.3 percent from 12.5 percent. Exxon became only the second U.S. business ever to report profits of more than $4 billion in one year; AT&T is the other firm and it passed $5 billion of earnings in 1978.

Exxon reported smaller profits in its U.S. oil refining and marketing operations in 1979 than in 1978, earning $294 million in 1978 and $113 million last year. But profits on its foreign refining operations jumped to $1.5 billion from $563 million in 1978.

Even though domestic oil production fell, Exxon's profits on this operation rose from $1.2 billion to $1.4 billion, mainly because uncontrolled Alaskan crude oil came into full production and the decline in output came among wells in the lower 48 states, where much of the output is subject to price control.

Other oil company earnings reported today included:

Sun Co., the 11th largest U.S. oil firm, said 1979 earnings were $700 million ($11.77 a share) vs. $415 million ($7.08) in 1978, with revenues up 42 percent to $10.8 billion. Fourth-quarter profits advanced more sharply to $223 million ($3.73) from $108 million $1.84).

Standard Oil Co. of Ohio, ranked 15th, said profits last year leaped 164 percent -- that largest percentage gain by major firms announced to date -- to $1.1 billion ($9.83 a share) from $450 million ($4) as revenues jumped 52 percent to $7.9 billion. Sohio is benefitting in particular from oil production at its Alaskan fields.

Marathon Oil Co., ranked 17th, said 1979 profits were $323 million ($5.34 a share) compared with $225 million ($3.73) the previous year. Sales rose 45 percent to $7.1 billion.