PITTSBURGH — Esmark Inc. said Wednesday that it has dropped its bid for U.S. Steel Corp. out of respect for the United Steelworkers, the Pittsburgh steelmaker’s union that has exclusively supported rival bidder Cleveland-Cliffs.

“The USW was our partner in the successful acquisition of Wheeling Pittsburgh Steel, and we remain close with them,” Esmark CEO Jim Bouchard said in a prepared statement.

The Sewickley-based firm went public with an all-cash offer valued at around $7.8 billion on Aug. 14, the day after Ohio-based Cleveland-Cliffs disclosed that it had the USW’s backing for a $7.3 billion proposal to take over the rival Pittsburgh steelmaker.

Esmark did not explain the timing of its decision to pull out of the bidding, given that the USW’s loyalty to Cliffs had been known since Aug. 13. That’s when Cleveland-Cliff’s published a letter that the Pittsburgh-based union had sent to U.S. Steel vowing that “it will not endorse anyone other than Cliffs for such a transaction.”

Esmark’s about-face came a day after Cliffs CEO Lourenco Goncalves demanded to know who else was bidding for U.S. Steel.

He said that right was assigned to Cliffs by the USW, which represents thousands of workers at both companies.

The union’s labor agreement with U.S. Steel gives it the right to bid on the company or on any U.S. Steel facility that receives a bid from another entity, and to be notified when such bids are being considered. Because the USW agreed to transfer that right to Cleveland-Cliffs, Goncalves said in a letter to the company that he expects to be notified “promptly” whenever U.S. Steel receives a bid.

Failure to notify would violate the steelmaker’s basic labor agreement with its union, Goncalves argued, ending his letter with a taunting ultimatum: Either fork over the proposals or acknowledge that the proposals don’t exist.

U.S. Steel said on Aug. 13 that it had received “multiple unsolicited proposals” to buy some or all of the business. That was the same day that Cliffs went public with its $7.3 billion offer it had made in late July. On Aug. 14, Esmark Inc. issued a news release disclosing its offer.

In the deal that Esmark cited Wednesday as a rationale for dropping its U.S. Steel bid, the Sewickley firm took control of Wheeling Pittsburgh Steel Corp. after a 2006 proxy fight.

Two years later, it sold the operations to Russian steel producer OAO Severstal for $1.25 billion. A few years after that, the business was sold again and eventually ended up in bankruptcy, where different companies picked off various facilities of the former Wheeling Pittsburgh Steel.

Outside financial and legal advisers are now helping U.S. Steel weigh its options. The company rejected Cleveland-Cliffs’ original buyout offer because the steelmaker wouldn’t sign a nondisclosure agreement before U.S. Steel agreed to the offered price.

New filings made public on Tuesday show that shortly after the rejection, Goncalves offered to sign a mutual nondisclosure agreement during the course of negotiations. He asked to meet face-to-face with U.S. Steel’s board of directors, saying “such a meeting would allow me to defend my thesis for how this deal benefits all parties involved.”

U.S. Steel CEO David Burritt responded the next day, thanking Goncalves for his willingness to keep talks private. As for the meeting, he said he’d have to confer with advisers to create a fair process for Cleveland-Cliffs and “other interested parties.”

The 122-year-old U.S. Steel had more than 22,000 employees worldwide at the end of last year, which includes 3,700 in southwestern Pennsylvania, where the company operates its Clairton, Edgar Thomson and Irvin plants, as well as its corporate office.

Shares of U.S. Steel dipped Wednesday afternoon following Esmark’s announcement that it was stepping away from the offer, but the stock recovered to end the day down about 2% at $31.32.