Spanish lender BBVA told Banco de Sabadell that it will not improve the takeover offer it has submitted for its smaller rival, Sabadell said Wednesday in a notice to the securities market supervisor.

BBVA Chairman Carlos Torres told Sabadell on May 5 that he felt it was very important for Sabadell's board to know that BBVA has no room to improve its financial terms.

The offer for all the shares of Spain's second-largest bank, presented last week, valued the country's fourth-largest lender at about 12 billion euros ($12.9 billion). The offer represented a 30% premium over Sabadell's price on April 29.

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

(1 dollar = 0.9306 euros)

(Reporting by Inti Landauro; editing by Jason Neely; Spanish editing by Mireia Merino)