U.S. Steel Corp. yesterday agreed to pay $4.3 billion to acquire Texas Oil & Gas Corp., one of the country's most profitable natural gas companies.

The merger would reduce basic-steel production to less than a third of U.S. Steel's business and is seen by analysts as a symptom of the sickness of the nation's steel industry.

The announcement yesterday is the latest step in an ambitious diversification campaign U.S. Steel launched four years ago when it acquired Marathon Oil Co. for $6.5 billion.

Approval of the merger with Texas Oil & Gas would give U.S. Steel, the nation's biggest steel producer, its second major property in the natural resources industry and make it one of the top 15 oil and gas producers in the nation, according to oil industry analysts.

Today, U.S. Steel is more of an oil company than it is a maker of metal for bridges, buildings and cars. Chairman David Roderick said yesterday that the company eventually could change its name, although there are no immediate plans to do so.

An estimated 54.1 percent, $7.9 billion of U.S. Steel's $14.6 billion in sales for the first nine months of 1985, came from oil and related businesses. By comparison, 34.9 percent, or $5.1 billion, of the company's revenue for the first three quarters of this year came from steel. The merger with Texas Oil & Gas, if approved, will reduce the percentage of revenue from steel even more.

U.S. Steel "seems to be reducing its percentage of steel sales further and further," said David Healy, an analyst with Drexel Burnham Lambert Inc. He said that the company's third-quarter 1985 results show why.

U.S. Steel reported an overall profit of $100 million (62 cents a share), on sales of $5 billion. That compares with profits of $153 million ($1.15), on sales of $4.7 billion in the year-ago period.

The "grinch" who stole income was the company's steel business, which reported third-quarter operating losses of $4 million on sales of $1.7 billion. By comparison, U.S. Steel's Marathon oil division reported third-quarter operating income of $344 million on sales of $2.7 billion, which was up from the previous year.

"The oil and gas industry may be having its problems. But the steel industry is in far worse shape," said Robert E. Phaneuf of Kidder, Peabody & Co. Inc.

Domestic steel companies have lost more than $6 billion since 1981, the steel industry's last profitable year. Those losses continued this week, with both U.S. Steel and Bethlehem Steel Corp. reporting income shortfalls in their steel-making operations.

Bethlehem, the nation's second-largest, vertically integrated steel maker, yesterday announced that it was omitting its quarterly common share dividend for the first time since 1939.

Overcapacity in the international steel market, increasing import penetration in the United States, changing materials needs in domestic automobile manufacturing and soft prices all mean that the domestic steel industry will continue to lose money in the foreseeable future, analysts said.

The figures show "that it's probably better to get out of the steel industry, or, at least, to reduce your holdings in that industry if you're going to be profitable," said Healy.

U.S. Steel's offer to buy Texas Oil & Gas makes sense in that light, Phaneuf said.

"Texas Oil & Gas is generally conceded to be one of the most efficient finders of natural gas in the business," Phaneuf said. The Dallas natural gas company spends about $1 per 1,000 cubic feet of natural gas it discovers. Other companies spend "anywhere from $1.30 to $1.50 per MCF (1,000 cubic feet)," Phaneuf said.

Texas Oil & Gas, a domestic and onshore company, last year ranked 14th in natural gas production.

Analysts say that because of its agility in the field and its conservative management, Texas Oil & Gas has been a consistent moneymaker since 1958, when it reported its first annual profit of $158,204 on sales of $1 million.

According to preliminary figures for its fiscal 1985, which ended Aug. 31, Texas Oil & Gas will earn $277 million ($1.32 per share) on sales of $1.7 billion. By comparison, the company earned $346.2 million ($1.65 per share) on sales of $2.1 billion in its 1984 fiscal year.

Under the terms of the tentative agreement reached yesterday, which must be approved by shareholders of both companies, shareholders of Texas Oil & Gas would receive 0.6333 share of U.S. Steel stock for each of their common shares. The gas company has an estimated 210 million shares outstanding with an estimated asset value of $17.42 a share. The stock exchange, as a result, would be worth about $3.6 billion.

But Phaneuf and other oil industry analysts interviewed yesterday said that Texas Oil & Gas would also transfer about $705 million in debts to U.S. Steel, thus boosting the estimated price of the deal to $4.3 billion.

On announcement of the merger agreement, which had been anticipated, Texas Oil & Gas stock fell 1 3/8 yesterday to 16 1/2 with 2,537,300 shares traded, while the price of U.S. Steel's stock fell 3/4 to 26 3/4 on volume of 2,883,100.