PARIS - French waste and water management company Veolia on Wednesday raised its offer for a 29.9% stake in Suez owned by Engie to 3.4 billion euros ($4 billion), and piled on the pressure for a swift outcome to its proposal.

Veolia has been trying to persuade Engie to part with most of its stake in Suez as a prelude to launching a full takeover bid for the utility, though Suez has pushed back vehemently against the approach.

Veolia said it had raised its offer to 18 euros per share from 15.5 euros per share, valuing the stake at 3.4 billion euros compared with 2.9 billion euros previously.

It added the offer was valid until the end of Wednesday, sticking to the original deadline of its offer to Engie.

But Veolia added it would only launch a subsequent tender offer for the whole of Suez with the blessing of the company's board, and offered a six month period during which to negotiate, should it acquire the 29.9% stake.

The French finance ministry has called on Veolia to demonstrate its approach to Suez is friendly. The state has a 23.6% stake in Engie, which in turn has 32% in Suez.

Suez shares were up 6.6% in early trading.

($1 = 0.8518 euros)

(Reporting by Dominique Vidalon, Matthieu Protard, Gwenaelle Barzic and Sarah White, editing by Louise Heavens and Mark Potter) ((matthieu.protard@thomsonreuters.com; +33-1-49495381;))