And the shortcomings involved are similar to those that Nordea and Handelsbanken have previously been punished for, according to the Swedish Financial Supervisory Authority (Finansinspektionen).
Journalist network OCCRP revealed to international media that banks across Europe appear to have been involved in a giant network of money laundering. Swedish banks Nordea, SEB, Handelsbanken and Swedbank were reportedly either used or attempted to be used in the movement of the money.
According the Guardian, documents show that at least $20 billion disappeared from Russia via the international bank system, but investigators believe it could amount to as much as $80 billion. The money is also suspected to have come from illegal activities.
Around 500 people are thought to be involved, including bankers from Moscow, oligarchs, people linked to the Russian government and spy agency FSB the Guardian writes, also naming Putin's cousin Igor Putin as sitting on the board of one of the Moscow banks involved.
Finansinspektionen's deputy general director Martin Noréus thinks the revelations confirm the authority's previous points about Swedish banks not doing enough to tackle money laundering.
"We can't comment on the individual transactions. But this seems to be about exactly the kind of shortcomings which emerged in the Panama Papers case," Noréus said.
Handelsbanken and Nordea previously had to pay fines for their inadequate handling of suspected money laundering between 2012 and 2014. Nordea says it has invested significant resources in order to stop the money laundering which is now being reported about however, where the money is thought to have moved between Moldavia, Latvia, Denmark, Sweden, the UK and other countries.
"We've improved our processes considerably in recent years. We have invested heavily in providing resources to improve controls. And we have a close dialogue with regulators," Nordea's press officer Petter Brunnberg told news agency TT.
SEB made similar comments, while Handelsbanken said it believes it reacted correctly, stopping the transactions when discovered.
"We take this very seriously. The transactions involved are four years old and well known to us. Necessary measures were taken," Handelsbanken press officer Johan Wallqvist said.