Hedge fund Elliott Management Corp said on Tuesday that all of its board nominees and all of Hess Corp's should make up a reconstituted board, a day after the activist investor rejected the oil producer's offer of two board seats.

The size and composition of the board is to be agreed upon, Elliott Management said in a statement.

Hess is scrambling to avoid an embarrassing defeat to Elliott at its annual meeting on Thursday. Elliott, which owns a 4.5 percent stake in Hess, is running a slate of five directors against Hess' nominees.

(Reporting by Swetha Gopinath in Bangalore; Editing by Sriraj Kalluvila)