UPDATE 1-Veolia to improve its offer for stake in Suez by Wednesday

(Adds Suez shares)

PARIS, Sept 28 (Reuters) - French utility group Veolia said on Monday it would improve its 2.9 billion euro ($3.37 billion) offer to buy the bulk of Engie’s stake in smaller rival Suez by Sept. 30.

Last month Veolia made its offer for a 29.9% stake in Suez owned by Engie, with a view to subsequently taking full control of Suez by buying up more shares.

Engie, which owns almost 32% of Suez, rejected Veolia’s initial advance but has said it would consider a higher offer.

Veolia’s CEO Antoine Frerot said on Friday that the company would increase its offer to buy a 29.9% stake in Suez and had the capacity to do so.

He also said Veolia’s offer remained valid until Sept. 30.

Suez shares were up 0.60% at 0729 GMT. ($1 = 0.8596 euros) ($1 = 0.8603 euros) (Reporting by Matthieu Protard; Editing by Kim Coghill and Susan Fenton)