Privately held steel company Esmark said on Wednesday it was scrapping its bid for U.S Steel Corp, respecting the United Steel Workers' support of rival Cleveland-Cliffs.

Last week, Esmark made an offer to buy U.S. Steel for $35 per share, or an equity value of $7.8 billion.

Esmark's exit leaves Arcelor-Mittal as the only known potential challenger to Cleveland-Cliffs, which went public with its bid for U.S. Steel earlier in August.

"The U.S. Steel board must go through their process that they previously announced (adding) we will evaluate any opportunities in connection with that process, subject to support from the USW," Esmark CEO Jim Bouchard said in a statement.

USW, which has asserted itself aggressively in the bidding battle, had said the union would not endorse any buyers other than Cleveland-Cliffs.

However, U.S. Steel last week said its labor agreement with USW does not afford the union the right to veto a sale of the company.

The future of U.S. Steel is important to Minnesota's Iron Range, where the major player is Cleveland-Cliffs, followed by U.S. Steel.