By Patricia Kowsmann

LISBON-- Isabel dos Santos, Africa's wealthiest woman and the second-largest shareholder of Portugal's Banco BPI SA, on Monday reacted to a takeover bid for that bank by a Spanish lender by suggesting another deal instead: a merger between BPI and Banco Comercial Português SA, Portugal's largest bank by capitalization.

Last month, Spain's Caixabank SA offered to buy the 55.9% of BPI that it doesn't already own for EUR1.329 a share in cash, pricing a deal at up to EUR1.09 billion ($1.24 billion). If successful, the Spanish bank would become the dominant bank across the Iberian peninsula.

The move by Ms. dos Santos, the daughter of Angola's president, complicates plans for Caixabank, which will be forced to raise its bid if it wants to succeed. BPI shares were trading up 7% at EUR1.46 on Tuesday. Shares of Banco Português were up 3% at EUR0.086.

A spokesman for Caixabank declined to comment.

On Monday, Caixabank Chairman Isidro Fainé said negotiations between Spain's No. 3 bank and BPI shareholders were still under way. "The game has just started," he told journalists in Barcelona.

That same day, Ms. dos Santos, who owns 18.6% of BPI through a vehicle called Santoro Finance, sent a letter to the bank, Banco Comercial Português and Caixabank laying out the reasons why BPI and Banco Comercial Português should discuss a merger. For one, the letter said, Caixabank's offer doesn't reflect the value of BPI.

The letter, signed by a Ms. dos Santos' representative who heads Santoro, said a diversified shareholder structure and an independent executive board would be in the best interest of BPI. It said a merger with Banco Comercial Português would form a large Portuguese bank with operations at home and in Angola, Mozambique and Poland.

It said Santoro has held talks with Banco Comercial Português shareholders. The lender's largest shareholder is Angola's state oil company Sonangol Group, with close to 20%.

In a statement, Banco Comercial Português confirmed it received the letter, and said it is "available to analyze" a possible merger if BPI shows interest.

A representative for BPI wasn't immediately available to comment.

A merger between BPI and Banco Português would create a lender 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 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.

BPI and Banco Português have lost money in 2014 as Portugal's economic crisis hit the ability of companies and families to service their debt. Charges over souring loans are falling, but lenders are struggling to find ways to return to profitability. They have both cut costs sharply in recent years. BCP, which required government aid to stay afloat, still has to repay EUR750 million in contingent convertible bonds to the state by 2016.

BPI, meanwhile, is trying to buy another Portuguese lender, Novo Banco SA, which was carved out from the collapse of Banco Espírito Santo SA.

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

Although BPI has kept quiet about Caixabank's offer, its relationship with the Spanish lender has been close along the years. After the offer was announced, BPI said Caixabank is "a shareholder since 1995, having maintained a permanent support for the growth strategy and affirmation of the BPI group in the last 20 years."

Jeannette Neumann in Madrid contributed to this article.

Write to Patricia Kowsmann at patricia.kowsmann@wsj.com

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