United States Steel Corp., the nation's largest steel producer and the 14th largest industrial company, yesterday reported a sharp decline in fourth-quarter and 1977 profits.

Responding to the news, directors slashed the firm's quarterly dividend by 28 per cent and stockholders unloaded Big Steel shares on the New York Stock Exchange.

Edgar Speer, chairman of U.S. Steel, issued a statement in Pittsburgh that blamed a "continuing flood of imports" for depressed profitability in the second half of the year. By December, he noted, imports accounted for 24 percent of domestic supply - a record level.

For the recent quarter, U.S. Steel actually suffered a pretax loss of $17 million. But a tax credit of $26 million brought total earnings to $9 million (11 cents a share) compared with $80.5 million (98 cents) for the 1976 period, as sales rose to $2.5 billion for $2 billion.

Profits for all of 1977 totaled $137.9 million ($1.66 a share), down sharply from $410.3 million ($5.03) in 1976, despite a $1 billion increase in sales to $9.7 billion. The 1977 annual profits included a $36 million tax credit, which Speer said represented a refund of past taxes, reflecting losses in 1977 for tax purposes.

Directors cut the cash payout on common stock to 40 cents a share from 55 cents, starting with a March 10 distribution to stockholders of record Feb. 10. Big Steel had been paying 55 cents a share quarterly since the second quarter of 1976.

Although Wall Street analysts had expected U.S. Steel to report higher earnings and had not anticipated a dividend reduction, there was no dramatic stock market reaction to yesterday's midday announcements.

U.S. Steel stock trading was halted at 12:26 p.m. and did not resume until just before the 4 p.m. close, permitting New York Stock Exchange specialists to balance buy and sell orders. For the day, U.S. Steel was the most active Big Board issue, down $3.50 a share to 28 7&8 on a volume of 660,000.

The Dow Jones average of 30 industrial stocks - including U.S. Steel - ended the day off 2.52, far less of a decline than a 19.75-point tumble last July 27, after No. 2 producer Bethlehem Steel cut its dividend in half and reported operating losses for the first six months of the year.

According to Roger Young, who follows the steel industry in New York for the investment firm of Dean Witter Reynolds, the price of U.S. Steel shares could decline further in trading over subsequent days. Young, who had forecast quarterly earnings of about 30 cents a share (vs. the actual 11 cents), said the industry's problems with improted products could be aggravated even more in the current quarter.

Responding to industry pleas, the Carter administration has established a plan to set minimum prices for imported steel in an effort to reduce cheap imports. But analysts said some American buyers have been purchasing large quantities of the imported steel in advance of the effective date of the administration program, which is expected to be about Feb. 15.

With the large volume of current imports followed by an expected sharp reduction in the second quarter, steel industry officials may have to wait until fall to determine the true impact of the U.S. government's plan, Young said.

Speer said his firm's performance in 1977 reflected not only the import situation but also a recently settled iron ore strike, a continuing strike at company coal mines and the sale of a company coal mines and the sale of a Bahamas-based subsidiary.

The dividend cut, he said, was "prudent" in light of the current situation and was related primarily to the low level of 1977 profits. Speer said steel shipments last year were 19.7 million tons vs. 19.5 million in 1976. Steelmaking operations failed to show a profit for the year but all non-steel business, which represents "substantial growing segments" of the company, was profitable, he added.

Two other steel producers yesterday also reported sharply lower 1977 earnings. National Steel, the third-largest manufacturer, reported profits fell 30 percent to $60 million ($3.12 a share compared with $86 million ($4.53) in 1976, despite a 10.5 percent sales gain to $3.1 billion.

Chairman George Stinson said, however, the National's fourth-quarter profits rose 9 percent to $16 million (85 cents) vs. $15 million (79 cents). He said the outlook for 1978 "is brighter and we believe it could be a good year."

Kaiser Steel Corp., the No. 12 producer, said 1977 earnings pinged to $4.5 million (51 cents a share) compared with $43.6 million ($6.06) million from $712 million. Kaiser suffered a fourth-quarter loss of $7 million compared with profits of $20 million a year earlier.

U.S. Steel said it spent $865 million for additional and replacement facilities last year, down from $957 million in 1976. The steel maker also announced a joint venture with Shell Oil to acquire and develop oil and natural gas leases off Louisiana and Texas.