The bank, which is one of the biggest in Scandinavia, was listed on Monday as having worked with Mossack Fonseca, the Panama law firm linked to a huge international tax investigation.
On Wednesday, Swedish broadcaster SVT reported that Nordea had recently loaned money, apparently for a construction project in Moscow, which ended up in a tax haven accessed by Serzhan Zhumashov, a close aide of President Nursultan Nazarbayev, who rules Kazakstan.
Nazarbayev has been at the helm of his country since 1989. He has been linked to numerous corruption cases and is accused of rigging multiple elections.
Nordea told Swedish reporters on Monday that while it did help some customers to create secret 'letter box' companies in tax havens in the past, it has since stuck closely to new stricter rules which were introduced in the wake of the global financial crisis in 2009.
The bank did not immediately respond to the latest accusations involving Kazakhstan, which are understood to have taken place in the years since banking regulations were tightened.
However plenty of Swedish commentators were quick to give their responses.
“This is about as bad as it can get,” said Albin Ränar, a spokesperson for the Swedish Shareholders' Association.
Meanwhile Jakob König, a financial expert interviewed by SVT, said he thought it was disgraceful that money deposited by ordinary Nordea customers was potentially being used to fund corruption.
“I do not think that there are many customers who would want their money used for this,” he said.
“The bank has reason to review its corporate culture,” Per Bolund, Swedish Minister for Financial Markets and Consumer Affairs, told TT.
The country's financial supervisory authority, Finansinspektionen, said on Monday it would launch a thorough investigation into Nordea's overseas activities.
Around 400 other Swedish individuals and businesses are also reported to have worked with Mossack Fonseca, which is known to have helped a range of leaders, criminals and celebrities around the world, using secretive offshore companies.
Sweden has a global reputation for high corporate and personal tax rates, which can reach 50 percent.