U.S. Steel said on Thursday that its labor agreement with United Steel Workers (USW) does not afford the union the right to veto a sale of the company that may arise from its recently announced strategic review.

U.S. Steel's statement came after USW said this week it would only back Cleveland-Cliffs Inc as a suitor for the company. The union said that "over the years, Cliffs has shown itself to be an outstanding employer to all of its workers."

U.S. Steel, which rejected Cliffs' $7.8 billion cash-and-stock offer as inadequate, has said it is exploring "multiple unsolicited proposals". It has attracted a $7.8 billion all-cash offer from Esmark Inc and as well as potential acquisition interest from ArcelorMittal SA.

In a regulatory filing, U.S. Steel said its agreement with the union gives it the right to counter with its own acquisition offer for assets covered under their bargaining agreement. If the union does not make an offer its board deems superior, U.S. Steel can sell itself to the bidder of its choosing.

USW representatives did not immediately respond to a request for comment.

(Reporting by Ananta Agarwal in Bengaluru; Editing by David Gregorio)