Last year, when the U.S. Steel Corp. pleaded before the federal government for relief from imports, critics of the nation's largest steelmaker pointedly asked why the government should bail it out when it insisted on investing in nonsteel activities rather than pumping profits back into its out-dated plants.

Yesterday the diversified giant made a bid for another nonsteel activity--Marathon Oil Co., at an estimated cost of $6.8 billion. The company, expecting criticism for investing money in an oil firm at a time when it is again complaining about the growing market share of steel imports, insisted yesterday it has not given up its commitment to steelmaking.

But the steel business has been a loser of late, suffering from slack demand because of the slumping economy and increased competition from foreign steelmakers. In order to continue to make steel, many companies feel they must make profits in other areas, such as the lucrative oil business.

"There's no return to be earned in putting money back into steel," said David Healy, a steel industry analyst with Drexel Burnham Lambert. "It's strictly financial diversification."

As one industry analyst pointed out yesterday, U.S. Steel's steel business accounted for 40 percent of its profits this quarter but will make up only about 25 percent if the acquisition is completed. A U.S. Steel spokesman had no response to a suggestion that the firm change its name from U.S. Steel to something else.

"Our tender offer will in no way diminish U.S. Steel's commitment to its steel operations," U.S Steel Chairman David M. Roderick said yesterday. "Our investment in those operations will continue as planned. This acquisition would achieve the major diversification that U.S. Steel has been seeking."

The steelmaker has been shutting down some steel plants during the last few years while modernizing others in an attempt to offset decreased steel demand, help it compete with cheap, high-quality steel from Canada and other countries and prevent losses such as the $293 million one in 1979. In that year the steel manufacturing unit reported a $102 million operating loss.

U.S. Steel already is big in chemicals, which grew from $21 million in profits three years ago to $71 million last year. At one time its competitors jokingly dubbed the company U.S. Chemicals.

The company is also big in coal and has ocean shipping operations that last year contributed $76 million in profits. In fact, the company is the 13th-largest owner of coal resources in the nation. Earlier this year it sold nearly one-fourth of its reserves but was still left with 2.4 billion tons.

Besides a natural gas company in the Pittsburgh area, it shares some oil drilling ventures with Pennzoil and Shell. U.S. Steel also manufactures oil and gas industry equipment and has a domestic transportation subsidiary.

In addition, the firm has sole or part ownership in mortgage banking, titanium products, a uranium company, stainless-steel products in Italy, a mining holding company in South Africa, a fertilizer firm in India and other metals operations around the world.

While the steel business is expected to grow an average of between 1 1/2 percent and 2 percent a year, "a significant portion of facility investments must be directed to those markets having above-average growth potential," Roderick said in the company's 1980 annual report. "In addition, a competitive rate of return must be realized wherever an investment is made."

The acquisition of Marathon in the long term would greatly improve the steelmaker's profits because of its growth potential. But in the short run it could hurt earnings slightly because of the billions of dollars involved in the proposed transaction. By the end of next year the acquisition should increase profits about 10 percent, Healy said.

"We see a very large expansion in Marathon's earnings and that could help their earnings," Healy said. "There's no attractiveness in investing in new steel plants."

Marathon could also benefit from the acquisition. It would be saved from the clutches of Mobil Corp. which also is vying for its assets, and it would be pretty much left alone because U.S. Steel is not yet savvy in the oil business.