The jostling between

Warner Music

(WMG)

and

EMI

is getting rougher.

On Wednesday, word emerged from EMI that Warner has twice offered to buy the British recording giant, with the latest offer coming in at $4.56 billion. EMI, which has its own offer on the table for Warner, rejected the proposals.

EMI previously floated an offer to acquire Edgar Bronfman Jr.-led Warner Music for $28.50 per share, or $4.2 billion. That offer was swiftly rejected by Warner's board. In a statement Wednesday, EMI said it raised the proposal to $31 a share -- and Warner rejected it again.

Warner's shares closed at $27.23 Tuesday.

In late May, EMI said it continues to believe "an acquisition of Warner Music by EMI would be very attractive to both sets of shareholders, but we will only pursue a transaction that delivers enhanced value and earnings accretion to our shareholders."

A joint group would create the world's third largest music company after Sony/BMG and Universal.