Activist investor Elliott's warning comes after Unizo had previously rebuffed an offer from Blackstone. The buyout group this week ratcheted up its pursuit of the company by launching the buyout offer, to which Unizo is still deciding its response.

"We strongly urge you to consider in good faith, and not unduly obstruct, the Blackstone proposal," Elliott, which owns 13.14% in Unizo, said in a statement.

It said Blackstone's offer of 5,000 yen is beneficial for shareholders and the employment conditions Blackstone has offered is "very generous to your employees".

A Unizo spokeswoman said the company is unable to comment on Elliott's statement.

Unizo was little known until travel services provider H.I.S. Co Ltd launched a hostile bid for it in July. Unizo ultimately rejected the bid but attracted the attention of other suitors who see the company as vastly undervalued.

But Unizo has played hard to get: Last week it rejected a proposal from Blackstone as well as one from an unidentified "locally renowned" fund.

This month Elliott ended weeks of silence and started to address its concerns about Unizo's disclosure to its board. That included seeking explanation on its sudden withdrawal of support for a bid from SoftBank Group-owned Fortress Investment Group.

Unizo originally welcomed the "white knight" bid from Fortress but later back-tracked.

In a separate statement, Fortress said it would extend its tender offer period until Nov. 1 from Thursday. It did not sweeten its bid of 4,000 yen a share.

Unizo shares closed at 4,940 yen on Thursday.

(Reporting by Junko Fujita; Writing by David Dolan; Editing by Muralikumar Anantharaman)

By Junko Fujita