TORONTO, Dec 7 - Cosmos Capital Inc, a Canadian private equity group, said late on Monday it withdrew from a bidding war for the nation's largest domestic advertiser, Cossette Inc, four months after its first bid was rejected.

Essentially Cosmos is not going to be submitting a superior bid and it has withdrawn its current offer, said Cosmos spokeswoman Sylvia Morin.

Cosmos offered to buy the struggling Canadian advertiser for C$4.95 a share in July, and then raised that to C$5.25 a share and then C$7.87 last month.

Last week Cossette Inc said it accepted a sweetened bid from U.S. private equity group Mill Road Capital for C$8.10 a share, or C$135.3 million ($129 million), and recommended again that shareholders reject the unsolicited takeover proposal from Cosmos Capital.

But Cosmos, whose principals include former founders of the ad agency, will not walk away empty handed, as Cossette's share price has risen from C$3.25 when the bidding war began to C$8.09 at the close on Monday.

Cossette, which serves major transnational clients, including McDonald's, Bell Canada, General Motors and Coca-Cola, has offices in Canada, Britain, the United States and China.

($1=$1.05 Canadian) (Reporting by Pav Jordan; editing by Peter Galloway)

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