* Fresenius says will "for the time being" refrain from bid
* Rhoen says regrets move, says merger with peer makes sense
* Fresenius says plans to lift Rhoen stake above 5 percent
* Rhoen shares down 22 pct (Adds background, details, shares)
FRANKFURT, Sept 3 (Reuters) - German healthcare conglomerate Fresenius has dropped its attempt to take over Rhoen-Klinikum after two other companies bought stakes to block the 3.1 billion-euro ($3.9 billion) merger of Germany's two biggest private hospital operators.
Fresenius said on Monday it has decided not to launch a renewed takeover offer "for the time being" but did plan to raise its stake in Rhoen to above 5 percent, a level which would put it on a par with its two antagonists, rival hospital operator Asklepios and hospital supplies firm B. Braun.
Rhoen shares were down 22 percent at 15.00 euros by 1108 GMT, while Fresenius's shares were up 2.1 percent at 87 euros.
Had the deal gone through Fresenius would have folded smaller rival Rhoen into its own hospitals unit Helios, creating a dominant private-sector hospital chain in Germany with about 6 billion euros in annual sales.
But in June Asklepios, the third-biggest operator, announced it had bought more than 5 percent of Rhoen, shocking many merger arbitrage hedge funds who had in April piled into what then looked to be a straightforward deal, despite it requiring 90 percent approval from Rhoen's shareholders to go ahead.
Subsequently it emerged that B. Braun, which competes with Fresenius in supplying medical equipment such as infusion and feeding tubes and dialysis machines, had also bought a 5 percent stake in Rhoen. The group was seen as being against the tie-up because it risked losing an important client if Rhoen became part of Fresenius's hospitals division.
"We regret that our public offer was blocked without providing a constructive alternative," Fresenius's chief executive Ulf Schneider said on Monday.
Asklepios's founder Bernard Broermann viewed a takeover of Rhoen by Fresenius as a threat to his own company's growth strategy, according to a banking source who knows Broermann well.
"We remain long-term investors. Our plans have not changed," an Asklepios spokesman said on Monday.
CROSSING THE THRESHOLD
The unusually high acceptance threshold of 90 percent was originally introduced by Rhoen's founder and chairman Eugen Muench to protect the company from hostile bids but ironically it proved insurmountable after he initiated the merger deal with Fresenius earlier this year.
Although caving in for now, Fresenius said on Monday it would raise its stake in Rhoen to slightly above the of current level of 5 percent minus one share.
One person familiar with the company's thinking said Fresenius would remain open to renewed merger talks but this could be a matter of having to wait three to four years.
Fresenius was in intense negotations with Rhoen throughout August over the terms of a fresh bid, which would have seen Fresenius aiming to buy just over 50 percent of Rhoen's shares.
But that would have limited Fresenius's opportunities for full merger synergies.
The complexities of any new deal, which sources said envisaged the creation of several joint ventures as a means to cutting duplication at the two groups, ultimately put Fresenius off.
"All our investments must add value, with manageable risks. After thorough analysis, we have therefore reached the conclusion that a new offer cannot be justified," Schneider said on Monday
Rhoen's executive board, which in June had been won over by Fresenius and Muench to back the tie-up, said it regretted Fresenius's decision.
"The Management Board continues to consider it logical from the strategic point of view to merge two large private clinic operators in Germany," said Rhoen's chief executive Wolfgang Pfoehler.
Rhoen is "well positioned for the future to continue playing an active role in the consolidation of the hospital market," he added.
Even though Fresenius-Rhoen would have had only 8 percent of the public-sector dominated German hospital market, the combined group would have been the only private player offering a hospital within an hour's drive to 75 percent of Germans.
Private operators have grown by taking over underfunded hospitals from debt-laden German municipalities and then seeking to improve operational efficiencies, despite political opposition to privatisation in the healthcare sector. ($1=0.7933 euros) (Andreas Kroener and Frank Siebelt; Editing by Greg Mahlich)