By Patricia Kowsmann and Jeannette Neumann

LISBON--Spain's Caixabank SA said Friday that its offer for Portugal's Banco BPI SA is "fair" and will stay on the table, escalating tensions in a high-profile, cross-border takeover bid.

Caixabank's remarks follow a statement Thursday night from BPI's board that said the Barcelona-based lender's EUR1.09 billion ($1.21 billion) offer wasn't enough, urging shareholders to reject it.

Caixabank, one of Spain's biggest banks, said in a regulatory filing that it will move forward with the offer "until its completion," quashing hopes for now of a raised bid.

Caixabank offered in February to buy the 55.9% of Portuguese lender BPI that it doesn't already own for EUR1.329 a share in cash. Shares of BPI closed Thursday at EUR1.46.

On Thursday, BPI's board said that under its calculations, BPI was valued at EUR2.04 a share. That excludes an extra EUR0.22 a share from synergies expected under the merger.

BPI's stock has risen sharply this week after another shareholder publicly rebuked the Caixabank offer and said BPI should consider merging with Portuguese lender Banco Comercial Português SA instead.

Isabel dos Santos, Africa's wealthiest woman and BPI's second-largest shareholder with a 18.6% stake, said a merger with Banco Comercial Português would create a large domestic lender with operations in Angola, Mozambique and Poland and a diversified shareholder base. She also said Caixabank's offer didn't reflect the value of BPI.

BPI didn't comment on the remarks from Ms. dos Santos, who is the daughter of Angola's president. Banco Comercial Português, whose largest shareholder is Angola's state oil company, Sonangol Group, said Tuesday it was "available to analyze" a possible merger if BPI shows interest.

Caixabank said Friday that shareholders can't analyze the benefits or disadvantages of such a merger "as the terms of such transaction have not been unveiled."

Caixabank's offer comes as BPI considers its own bid for Novo Banco SA, the lender that was carved out from the collapse of Portugal's Banco Espírito Santo SA.

If Novo Banco were to be purchased by BPI and BPI in turn were swallowed up by Caixabank, that would transform Caixabank into the largest lender in Portugal, with a roughly 28% market share of assets and loans.

Such a foothold in Portugal would convert Caixabank into the dominant lender across the Iberian peninsula. The Spanish bank has the most bank branches and the largest market share in Spain.

A merger between BPI and BCP would also create a domestic giant, with a market capitalization of EUR6.5 billion and assets of EUR120 billion. BPI is Portugal's No. 4 bank in terms of assets, and BCP is No. 2, after state-owned Caixa Geral de Depositos SA. Both lenders have operations abroad, including in Angola, where BPI controls 50% of Banco de Fomento Angola SA.

Through a spokesman, Ms. dos Santos said the merger of the two would "bring back a sentiment of ambition to Portugal's financial system," which has been hard hit by a three-year sovereign-debt crisis and the collapse of Banco Espírito Santo SA last year. Caixabank's offer, she said, makes the bank Iberian, but less Portuguese.

Write to Patricia Kowsmann at patricia.kowsmann@wsj.com and Jeannette Neumann at jeannette.neumann@wsj.com

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