By Patricia Kowsmann

LISBON-- Banco BPI SA's board on Thursday shot down a EUR1.09 billion ($1.21 billion) takeover offer from its largest shareholder, Spain's Caixabank SA, saying it undervalues the company.

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.

BPI's board said that under its calculations, BPI is valued at EUR2.04 a share. That excludes an extra EUR0.22 a share from synergies expected under the merger between the banks. Therefore, BPI said, "it doesn't recommend that its shareholders accept the bid."

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 Ms. dos Santos's remarks.

Banco Comercial Português said Tuesday it is "available to analyze" a possible merger if BPI shows interest.

A representative for Caixabank declined to comment.

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 greatest number of bank branches and the largest market share within Spain.

--Jeannette Neumann in Madrid contributed to this article.

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

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