Ramsay Generale, 50.9 percent owned by Australia's Ramsay Health Care, lifted its bid to 58 Swedish crowns per Capio share. An initial bid of 48.50 crowns had been quickly rebuffed by Capio's board and several of its largest investors in July

Capio's board said in a statement it would evaluate the new offer and give its formal opinion on it "in due course".

Shares in Capio, which runs clinics and hospitals in Sweden, Norway, Denmark, France and Germany, rose more than 11 percent to 56.60 crowns in Stockholm on Monday. Shares of Ramsay Generale were down 3.7 percent.

Capio has said it is planning to focus its business on its core markets in the Nordics, a repositioning it believes will drive shareholder value.

Healthcare remains primarily financed through taxes in Capio's Swedish home market but private players are increasingly involved in providing the actual services.

R12 Kapital, Capio's second largest shareholder declined to comment to Reuters, while Swedbank Robur and the Fourth Swedish national pension fund, two other top investors, where not immediately available for a comment.

Several media groups, including Reuters, had reported Ramsay was considering revising its bid.

"Our revised offer is highly financially compelling for Capio's shareholders," Ramsay Generale CEO Pascal Roche said in a statement.

"It also provides Capio's shareholders with an attractive alternative to the disposal of Capio France with certainty on

valuation as RGdS’(Ramsay Generale) offer is integrally in cash."

Since the initial bid Capio has announced plans to sell its French business to Ramsay Generale's rival Vivalto Sante, but that deal, which has an upfront enterprise value of 425 million euros ($488 million), is partly subject to shareholder approval at a meeeting on Oct. 18.

Ramsay said on Monday it had decided to waive a bid condition regarding clearances from competition authorities, while adding they expected clearance from the French Competition Authority to be obtained by October 15.

Ramsay also said it reserved the right to waive one or more of the conditions for a completion of the bid, including to complete the offer at a lower acceptance level than 90 percent.

The company is planning to use the funds from its proposed sale of Capio France to pay down debt, return cash to shareholders, and invest in areas such as digitalization.

(Reporting by Johannes Hellstrom; editing by Jason Neely/Keith Weir)