Negotiations between USX Corp. and the United Steelworkers union were suspended yesterday, raising the prospects for a strike at the nation's largest steel producer when the current labor contract expires at midnight tonight.

David M. Roderick, chairman of USX -- the renamed U.S. Steel Corp. -- yesterday rejected the steelworkers' offer of a wage freeze, saying the company would have to receive reductions in wages and other labor costs comparable to concessions that other U.S. steel companies have received this year.

"We will not accept anything but a competitive labor agreement," Roderick said. "Not that we want to be tough and disagreeable -- we just can't do anything less."

Spokesmen for USX's 45,000 union workers countered that they cannot agree to further labor cost concessions until USX agrees to provide more detail on its financial condition -- information that Roderick called confidential.

That left both sides apparently locked in place, "waiting for the other one to blink," as one steel union official put it yesterday.

For the steel industry, which has had only one major strike since 1959, a long shutdown at USX would add to the turmoil caused by the recent bankruptcy petition filed by LTV Corp. and heavy continuing losses suffered by major producers.

James N. McGeehan, treasurer of the United Steelworkers and chief negotiator, said USX does not require the labor cost reductions other companies have received because its costs already are the lowest among the major producers.

"The union knows better than the company what the total employment costs are of the major steel producers," he said. "Those companies, unlike USX, turned over to us their books . . . or offered them to us."

McGeehan said steelworkers account for only 20 percent of USX's costs. "We're willing to seriously attack our 20 percent, but we're not willing to enter into an unconditional surrender so that the other 80 percent can be satisfied," he said.

The steelworkers' objective is to fine-tune labor contracts with the major companies to put all of them in a comparable competitive position. "We don't believe in competition being uneven, in terms of compensation or prices for products," a spokesman said.

Roderick said the union has received a certified financial accounting of USX. "They fully realize that the steel industry has been operating at a substantial loss for an extended period of time . . . and those losses are continuing." USX's steel operations, about one-third of its business, had an operating loss of $42 million in the second quarter.

As the two sides traded barbs about USX's financial condition, the company continued preparations for an extended strike, shutting down coke batteries and other facilities. Roderick warned that some of those shutdowns may be permanent.

Roderick said the company wants to cut its labor costs, including wages and benefits, by $2 to $3 an hour to a level of around $23, concessions that would match those at other major companies, he said. The average hourly wage in the steel industry is nearly $14 an hour.

Meanwhile, Bethlehem Steel Corp. yesterday reported a net loss of $23.8 million for the second quarter of 1986, compared with net income of $20.4 million (30 cents per share) for the same period last year. Sales for the quarter were $1.2 billion, an 8 percent drop from $1.3 billion reported for the second period in 1986