TOKYO (Reuters) - Unizo Holdings 3258.T said Monday it would continue talks with Blackstone Group BX.N and SoftBank-backed 9984.T Fortress Investment Group on a potential takeover, raising the possibility of a bid battle between the two global buyout firms.

FILE PHOTO: The ticker and trading information for Blackstone Group is displayed on the floor of the New York Stock Exchange (NYSE) April 4, 2016. REUTERS/Brendan McDermid

Potential rival bids from Blackstone and Fortress would mark another twist in the takeover saga surrounding the once-obscure hotelier, now seen as a test case for Prime Minister Shinzo Abe’s push for greater transparency and corporate disclosure.

Blackstone last week told Unizo it would launch a tender offer at 5,000 yen ($46.05) a share and said it would consider other options, including initiating a bid, if Unizo did not agree to the conditions by Wednesday.

“We have carefully evaluated and considered Blackstone’s offer. And today all the board members agreed to continue talks with Blackstone as its proposals could help maintain and improve corporate value and secure shareholders benefit,” Unizo said in a statement.

Unizo said separately on Monday it would also continue talks with Fortress, which in August emerged as Unizo’s white-knight bidder. But in September, Unizo had withdrawn its backing for Fortress.

Unizo said it had asked Fortress to raise its offer price to 5,000 yen a share, the same as Blackstone’s offer, from 4,000 yen. Unizo said Fortress had said it was ready to discuss improving the bid.

Unizo had said previously that Fortress did not respond to a

request to raise its offer price to 5,000 yen from 4,000 yen. Unizo shares closed at 4,960 yen on Monday.

Last week, Fortress had said it would extend its tender offer period for Unizo for a third time to Nov. 1.

A Tokyo-based Fortress representative declined to comment on Monday. A Hong Kong-based Blackstone spokeswoman was not immediately available for comment.

Unizo has already rejected other buyout proposals from Blackstone as well as one from a “locally renowned” fund that it did not identify.

In July, Unizo became the target of a hostile bid from a travel agent H.I.S. Co 9603.T.

Last week, Unizo’s biggest shareholder Elliott Management had pushed Unizo to accept Blackstone’s offer, saying the offer of 5,000 yen was beneficial for shareholders.

But Unizo is continuing to demand certain conditions that both Blackstone and Fortress have not agreed to.

Unizo said it had asked both Blackstone and Fortress to allow it to create an entity that would have veto rights over the timing and method of a future exit of Blackstone.

Unizo also said it had also asked the both funds not to break up the company.