Exxon Corp., the world's largest oil company, reported yesterday that profits in the third quarter of 1979 were $1.14 billion, up 120 percent from the same period last year.

The company said that most of the gain came from operations overseas, where crude oil prices are being passed on more rapidly than here. But third-quarter figures also showed that Exxon's refining and marketing profits in the United States increased substantially from depressed levels earlier in 1979.

Exxon's numbers -- the July-September profits came on worldwide sales of $20.6 billion -- are expected to be matched by healthy earnings gains for other major oil companies and fuel the political debate over petroleum profitability.

Atlantic, Richfield Co. said yesterday its third-quarter profits were up 45 percent, while Standard Oil Co. of Indiana (Amoco) said last Firday its earnings rose 49 percent.

White House Press Secretary Jody Powell cited the Exxon profits yesterday as evidence that President Carter's proposed "windfall" tax on oil profits "must be and can be" strengthened on the Senate floor and in conference committee with the House.

The "windfall" that this tax is intended to recapture has not even occurred yet. It will come as federal price controls on domestic oil are lifted over the next two years.

On Friday, the Senate Finance Committee approved a version of the proposal that would bring in an estimated $141.7 billion in new taxes between now and 1990, compared with $273.4 billion in a House bill and Carter's proposed $292 billion.

Powell said the "message from the profits is clear: We need the windfall profits tax." Separately, Carter told a group of citizens that the House version is "very acceptable" while the Senate Finance Committee bill is a "good beginning . . . but it is not adequate." Carter made no direct reference to oil industry profit reports.

This was the first time Exxon's profits have exceeded $1 billion in any quarter, but not the first time for any U.S. company. American Telephone & Telegraph and General Motors both have had $1 billion quarters.

Exxon's third-quarter profits equalled $2.60 a share of common stock compared with $525 million ($1.18 a share) in the same period of 1978, when revenues were $15.9 billion.

For the first nine months of this year, Exxon profits rose 55 percent to $2.93 billion ($6.64 a share) from $1.91 billion ($4.28) in the same period a year earlier. Revenues increased 26 percent to $59 billion.

In the third quarter. Exxon's world-wide profits included a one-time gain of $200 million because of reduced tax liabilities in Britain, after passage of new legislation there. In addition, because of foreign exchange fluctuations in Exxon's international business, the company had $127 million in currency losses in the recent quarter compared with a loss of $178 million in the same quarter last year.

Pretax profits from domestic refining and marketing operations, for Exxon rose more than 30 percent in the recent quarter to $112 million from $85 million a year ago.

But, because of depressed earnings from domestic operations earlier in 1979. U.S. refining and marketing profits for the first nine months were down 17 percent to $180 million from $217 million. Total U.S. petroleum and natural gas earnings rose modestly in the first nine months to $1.17 billion from $1.14 billion.

In a recent letter to Carter, Exxon chairman Clifton Garvin said his firm was selling No. 2 heating oil at a level some 5 percent below the industry average. Additional Exxon data provided recently to government authorities showed that regular gasoline was being sold at wholesale for 67.7 cents a gallon on Sept. 1 compared with 45.7 cents at the beginning of the year, an increase of about 48 percent.

Company officials have testified that these increases are below those of most competitors and are evidence of "restraint" in passing along real cost increases. World oil prices have increased an average of 60 percent since Jan. 1 because of price increases by oil-exporting nations and the adverse impact of the Iranian revolution.

Although Exxon data show restraint in domestic gasoline and heating oil prices, the recent increases in profitability have boosted two key measures of a compnay's performance. In the first nine months, Exxon's return on captial invested in the firm was at an annual rate of 15.3 percent compared with 11.6 percent a year ago. Return on stockholders' investment (equity) in Exxon was 18.5 percent, up from 13 percent a year ago.

Atlantic Richfield, No. 7 in the U.S. industry, reported third-quarter profits of $320 million ($2.60 a share ) compared with $220.5 million ($1.81) a year ago, as sales increased to $4.4 billin from $3.4 billion.