* BBVA submits offer directly to Sabadell shareholders

* Sabadell's board rejected previous offer on same terms

* BBVA offers one of its own share for every 4.83 Sabadell shares

* BBVA sees costs savings of 850 million euros

* Sabadell shareholders to get 16% stake in combined bank

MADRID, May 9 (Reuters) - Spanish bank BBVA presented a 12.23 billion euro ($13.11 billion) takeover offer for rival Sabadell directly to shareholders on Thursday, turning to a hostile bid after Sabadell's board rejected the same proposal this week.

BBVA's decision comes after Sabadell's board on Monday said the unsolicited bid significantly undervalued the bank's potential and growth prospects. The board repeated that position on Thursday.

"We are presenting to Banco Sabadell's shareholders an extraordinarily attractive offer to create a bank with greater scale in one of our most important markets," said BBVA's Executive Chairman Carlos Torres Vila.

Hostile takeover bids are rare in European banking. A recent example is Intesa's successful takeover of UBI Banca in 2020.

Shares in BBVA fell 5% in early trading, while Sabadell shares rose 5.5%.

"In our view, the deal is now a question of price and that both banks negotiate and abandon the hostile route," Alantra analysts said in a note, adding that it remained to be seen whether Sabadell would be willing to negotiate.

"In our view, a hostile bid could be a lose-lose for both banks. Sabadell would defend itself, but the damage to the franchise remains to be seen as this could be a lengthy process," they said.

The Spanish government opposes the hostile takeover bid, a source at the Economy Ministry said.

BBVA, Spain's second-biggest bank by market value after Santander, offered an exchange ratio of 1 newly issued BBVA share for every 4.83 Sabadell shares, a premium of 30% over April 29 closing prices.

COST SAVINGS

Spanish banks have been looking for ways to increase revenue as a boost from high interest rates begins to fade.

BBVA aims to create a lender with more than 100 million customers globally and assets exceeding 1 trillion euros, second only to Santander among Spanish banks.

It is the second attempt at a tie-up between BBVA and Sabadell. They called off merger talks in November 2020 after failing to agree on terms, including the price tag.

Sabadell has a large retail shareholder base accounting for almost half of its shares, with big institutional owners including BlackRock and Dimensional Fund Advisors.

Buying Sabadell would allow BBVA to diversify from Mexico, its main market, and other developing economies such as Turkey and South America and focus on its domestic market.

BBVA Chief Executive Onur Genc said, "all stakeholders will benefit from this operation."

"Banco Sabadell has done an excellent job, with remarkable progress in recent years, and now its shareholders can join an entity with an unparalleled combination of growth and profitability in Europe," Genc said.

The deal, which BBVA estimates could bring cost savings of 850 million euros before taxes, would give Sabadell shareholders a 16% stake in the combined lender.

The combined entity would overtake Caixabank as Spain's biggest domestic lender with over 625 billion euros in assets in the country, compared with Caixabank's just over 574 billion euros.

Spain's banking sector has seen a period of consolidation as lenders seek to cut costs and boost scale. Spain now has 10 banks, down from 55 before the start of the 2008 global financial crisis.

($1 = 0.9307 euros) (Reporting by Jesús Aguado; Additional reporting by Emma Pinedo, Inti Landauro, Belen Carreno in Madrid and Andrés González in London; Editing by Aislinn Laing, Christopher Cushing and Susan Fenton)