PARIS, March 21 (Reuters) - Waste and water management company Veolia on Sunday rejected a proposal by Suez to negotiate a takeover if the two companies agreed on the sale of most of Suez's French assets to investment funds Ardian and Global Infrastructure Partners (GIP).

Ardian and GIP said earlier on Sunday they were offering 11.9 billion euros ($14.2 billion) for parts of Suez's business - primarily its water and waste assets in France, and some broader water activities globally.

The stand-off marks the latest twist in a long-running and increasingly bitter takeover tussle between Suez and Veolia, which are struggling to agree how to carve up Suez's buiness and have clashed in court over the saga.

The companies, rivals dating back to the 19th century, manage most of France's water networks.

Suez has rebuffed a 11.2 billion euro ($13.33 billion) bid from Veolia, its top shareholder with 29.9%, saying it undervalued the company, and rejected arguments that, as a combined force, the companies would be better placed to take on global competitors.

Suez said in a statement on Sunday the alternative proposal involving Ardian and GIP could offer a way out.

It said its board had welcomed the offer, and it set various deadlines for Veolia to come to the table, saying it would accelerate its strategic plan, which includes asset sales, if no deal is reached by April 20.

"We now have a solution, supported by a new proposal from Ardian–GIP, which would enable the two companies to finalise an agreement in the interest of all the stakeholders," Suez Chairman Philippe Varin said in a statement.

But Veolia said it was "not interested" in what it called a dismantling of the group.

Ardian and GIP's offer is equivalent to 20 euros per share based on an enterprise value of 15.8 billion euros, Suez said, above the 18 euros per share offer by Veolia for the whole of Suez.

Veolia proposed on March 10 to sell all of Suez's French activities to infrastructure fund Meridiam, one solution it had put forward to try to pre-empt any anti-trust problems and to leave Suez with some business.

Veolia said its takeover bid was irrevocable and its proposal was "the best possible effort" to ensure what would remain of Suez had sufficient size to develop, including outside France.

Ardian and GIP had shown interest in the past but had not made a formal bid. ($1 = 0.8405 euros) (Reporting by Sybille de La Hamaide and Sarah White; editing by David Evans and Barbara Lewis)