SVT's allegations were based on leaked suspicious activity reports (SARs) filed by banks and other financial firms with the U.S. Department of Treasury's Financial Crimes Enforcement Network (FinCEN), which were reported by U.S. and other media on Sunday.
"The fact that there has been suspected illicit financial flows through SEB in the Baltic region is something that has been reported on...so in that sense this information is not new," the FSA told Reuters.
The Baltic scandal, first ensnaring Danske Bank and resulting in a record Swedish fine for Swedbank, lifted the lid on money flows from Russian and other non-resident clients into the European Union and elsewhere.
"The information that (SVT's) Uppdrag Granskning presents in its programme does not contain any news for the bank," SEB said in a statement.
SEB was fined 1 billion crowns by Sweden's financial watchdog in June for failures in compliance and governance in relation to anti-money-laundering controls in the Baltics.
"The scope in time on our part for the investigation was originally set for 2007-2019, but for a number of reasons...not least changes in the regulatory framework...that time frame was later limited to 2015-2019," the FSA said.
Shares in SEB were up 2.1% at 1141 GMT.
"It doesn't add much that is new. We talked about a relatively large number of suspicious transitions before," said Andreas Hakansson, a senior analyst at Danske Bank.
Hakansson added that the SVT programme did, however, contain some new details on names connected to suspected wrongdoing at SEB.
Among others, SVT said SEB did business with a British company that was part of the so-called "Russian laundromat", an alleged large-scale, Russian-led money laundering scheme reported by media in 2017.
The FinCEN leaks reported by media on Sunday showed several global banks moved large sums of allegedly illicit funds over a period of nearly two decades despite red flags about the origins of the money.
($1 = 8.9257 Swedish crowns)
By Colm Fulton