U.S. Steel Corp. yesterday reported lower second-quarter profits compared with last year, but Chairman David M. Roderick said the company would start paying higher dividends to its shareholders.

Xerox Corp. reported income rose 35 percent in the second quarter, excluding results from units of the company that are being sold or were discontinued, and predicted its third and fourth quarters also would be strong because of increased photocopier sales.

*U.S. Steel earned a profit of $133 million (93 cents a share) on sales of $5.1 billion in the second quarter of 1985, compared with a profit of $140 million ($1.04) on sales of $4.9 billion in the second quarter of 1984. The 1984 figures include $27 million (26 cents) in extraordinary gains from the early repurchase of debt.

Roderick announced that company directors had declared a dividend of 30 cents a share on common stock, payable Sept. 10, 1985, to stockholders of record at the close of business on Aug. 9. The dividend of 30 cents a share compares with a 25-cent dividend declared regularly since the fourth quarter of 1982.

"Second-quarter results clearly demonstrate the effectiveness of our ongoing efforts to operate our businesses more efficiently, especially in light of the lower prices in many of the markets we serve, and fewer benefits from extraordinary gains and asset sales compared with the second quarter last year," Roderick said.

Steel and related resources generated operating income of $85 million on sales of $1.8 billion in the second quarter of 1985, compared with income of $84 million on sales of $1.8 billion in the second quarter of 1984.

*Xerox had income from continuing operations of $118 million ($1.11 a share), up from $88 million (79 cents) a year ago.

The figures exclude operating results from Xerox's six publishing units, which are being sold, and a loss from discontinued operations. Including these operating results, second-quarter net was $96 million (87 cents).

In the first half, income from continuing operations was $234 million ($2.19), up 6 percent from $222 million ($2.07) a year ago.

Revenue in the second quarter was $2.14 billion, up from $2.08 billion a year ago, and amounted to $4.1 billion in the six-month period, up from $4.08 billion in the comparable period a year ago.

The strong U.S. dollar cut six-month revenue by about 7 percent, the company said.

*Uniroyal Inc. reported its net income fell in the second quarter to $26 million (72 cents a share), including an extraordinary charge of $9 million. That compares with $30 million (86 cents) in the same quarter of 1984. Sales for the quarter fell to $557 million from $586 million a year ago.

For the first six months of 1985, net income was $47 million ($1.30), compared with a net loss of $9 million in the first half of 1984. Sales for the half totoled $1.07 billion, virtually unchanged from $1.1 billion in the year-ago period.