By Scott Murdoch and Byron Kaye

(Reuters) - U.S. online property giant CoStar Group (NASDAQ: CSGP ) has proposed to buy Australia's Domain Holdings for A$2.65 billion ($1.7 billion), the real estate classifieds group said on Friday, sending its shares up as much as 45%.

Domain said CoStar had bought a 16.9% stake in the company on Thursday and proposed to buy the rest of the shares at A$4.20 per share in cash, a 34.6% premium to its closing share price on Thursday which the Australian company said it is considering.

The news sent Domain shares up as much as 45% to A$4.28 in early trading, their highest level in three years and above the offer price.

Domain is about 60% owned by Australian media group Nine Entertainment and its shares rose 17% on the CoStar offer.

Shares of REA Group, seen as Domain's only competitor in the Australian market, dropped 12% in early trading, while shares in REA Group's majority shareholder News Corp (NASDAQ: NWSA ) slid 7%.

Backing from a major U.S. firm for a struggling Domain would make it a more powerful competitor against REA, the market leader for property classifieds.

The deal, which would require Foreign Investment Review Board approval, would be CoStar's first time owning an Australian asset.

($1 = 1.5608 Australian dollars)