MADRID, May 8 (Reuters) - Spanish lender BBVA has told Banco de Sabadell it will not improve the all-share takeover offer it has made for its smaller rival, Sabadell said in a filing to the stock market regulator on Wednesday.

"I consider that it is very important that your Board of Directors knows that BBVA has no room to improve its economic terms," BBVA Executive Chairman Carlos Torres told Sabadell on May 5, Sabadell said in the filing.

The all-share offer from Spain's second-largest bank, unveiled last week, valued the country's No.4 lender at about 12 billion euros ($12.90 billion). The offer represented a 30% premium over Sabadell's price on April 29.

Sabadell's board on Monday rejected the takeover proposal saying it undervalued its potential and growth prospects.

($1 = 0.9306 euros) (Reporting by Inti Landauro; editing by Jason Neely)