* Investindustrial has until June 30 to make Club Med bid - AMF
* Closing date for current offer for Club Med extended - AMF
* Gaillon Invest has ruled out making higher bid for Club Med (recasts with AMF deadline statement, closing shares)
PARIS, May 27 (Reuters) - France's financial regulator has given Investindustrial Development, a fund led by Italian businessman Andrea Bonomi, until the end of June to launch a counter-bid for Club Mediterranee.
It also extended again, until an unspecified date, the deadline for Club Med shareholders to decide whether to accept a long-delayed 557 million euro ($758 million) offer by Chinese conglomerate Fosun and French private equity firm Ardian. The deadline had already previously been extended until June 6.
Should Investindustrial choose not to submit a bid for Club Med by 1600 GMT on June 30, it would be barred from making an offer for a period of six months, the regulator - the AMF - said on its website on Tuesday.
Funds led by Bonomi said on Monday they could make a counter-bid for Club Med, saying they would first need access to the French holiday group's books before making a decision.
Gaillon Invest, the investment vehicle behind the Ardian-Fosun bid, said earlier on Tuesday it did not plan to raise its takeover offer for Club Med despite a possible higher rival bid.
"Gaillon Invest has no intention of raising its offer above the 17.50 euro price, which represents a good price given what they know about the company and the market," a Gaillon spokeswoman said.
The AMF had asked for clarity on the funds' intentions towards Club Med after one of them, Strategic Holdings, became Club Med's top shareholder with a stake of more than 10 percent earlier this month.
Shares in the holiday group were still trading above the existing offer price on Tuesday, closing near a fresh five-year high of 19.60 euros.
($1 = 0.7345 Euros) (Reporting by Cyril Altmeyer; Writing by Dominique Vidalon; Editing by James Regan and Pravin Char)