By Jeannette Neumann 

MADRID-- Banco Santander SA said Tuesday that it will offer to buy out the 25% of its Brazil unit that it doesn't currently own, in a deal that could be worth up to EUR4.7 billion ($6.5 billion).

Spain's biggest bank and the euro zone's biggest lender by market value said it would offer a 20% premium over the last closing market price and expects to close the deal by October.

Santander said in a statement that the offer reflects the bank's "confidence in Brazil and its Brazilian subsidiary as well as the latter's long-term growth potential."

The news came shortly before Santander said that first-quarter net profit rose 8.1% to EUR1.3 billion, slightly above analysts' expectations. But total lending was down amid what Santander said was weak demand in Europe, particularly in Spain and Portugal.

Brazil and Mexico, which account for more than a quarter of Santander's net profit, experienced big declines. Santander's Brazil unit saw net profit fall 27% compared with a year earlier, while its Mexican unit posted a 43% drop. Net profit from its U.K. unit, which accounts for around one-fifth of the bank's profit, was up 68%.

Also, the bank said commissions and trading income were down overall.

Santander posted a EUR1.2 billion net profit for the first quarter of 2013. Analysts polled by data provider FactSet forecast net profit of EUR1.2 billion for the first three months of this year.

Santander also posted a better-than-expected first-quarter net interest income of EUR6.99 billion, a 3% decrease from the previous year. Analysts polled by FactSet anticipated net interest income of EUR6.6 billion this quarter.

The lender's rate of bad loans--those that were more than 90 days overdue--as a portion of total loans fell to 5.52% from 5.61% in the fourth quarter of last year. Santander said that was the first decline in the rate since 2007. In Spain as a whole, the bad-loan ratio notched up slightly to 7.61% from 7.49% in the fourth quarter of last year.

But Spanish lenders Caixabank SA, Banco de Sabadell SA and Bankia SA said in recent days that they had also seen a small decrease in their bad-loan ratios in the first quarter of this year compared with the fourth quarter of 2013.

Investors and analysts have been keeping close tabs on Spanish banks' bad-loan figures to test their progress in shedding liabilities that accumulated on their balance sheets during the financial crisis.

Mounting defaults by homeowners and companies forced Spain to request a bailout in 2012 and inject EUR41 billion of European Union funds into its most troubled lenders.

Still, Santander's bad-loan ratio for the first quarter of 2014 is above the 4.75% the bank reported for the same period a year earlier.

In Spain, the bank said total loans dropped from the previous year. But there was a slight increase in lending from the previous quarter, the first rise in five years, Santander said.

Write to Jeannette Neumann at jeannette.neumann@wsj.com

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