Veolia offered 18 euros per share, 30% above the market and remained alone in the running.
Ardian has not made a firm offer.
It is now up to Suez and Veolia to find common ground.
Veolia has undertaken not to conduct any hostile takeover bids on the rest of Suez's capital.
For its part, Suez has placed its water branch within a foundation under Dutch law to block its sale.
Veolia intends to sell it to the Meridiam fund, so as not to concentrate too many activities in the water sector to comply with European competition laws.
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