(Adds buyout details, context and background) April 6 (Reuters)...

(Adds buyout details, context and background)

April 6 (Reuters) - Private equity firm BGH Capital has proposed a revised A$8 per share buyout for Australia's Virtus Health (VRT) after the fertility services provider shunned its previous offer and accepted a sweetened bid from rival bidder CapVest Partners LLP.

BGH, which owns 19.9% of Virtus shares, proposed its new bid on Wednesday after the Australian in vitro fertilization (IVF) service provider recommended a cash offer of A$8.25 per share from CapVest to its shareholders via a scheme of arrangement.

Virtus has been the subject of months-long takeover battle between Melbourne-based BGH Capital and London's CapVest as both private equity firms are jostling to control the healthcare service provider, which has seen its share price surge 50% since before the bidding war started last December.

BGH's off-market takeover bid is at a discount of 0.9% to Virtus' last close on Tuesday, and structured as an all-cash offer, with no reliance on any tax rulings or capital returns, the private equity firm said.

The offer would provide shareholders with "an opportunity to divest as much Virtus stock as they deem appropriate" and without having to pay brokerage, BGH said.

Virtus' deal with CapVest allows its board to consider a superior proposal from Melbourne-based BGH or another party, hinting that the bidding war for the IVF service provider was not necessarily over.