* EBM says complaints highlight limited Swedish dealings
* Inquiry into possible insider trading rules breach ongoing
* EBM also continuing investigation into suspected fraud
* Swedbank shares rise 1.6 pct (Adds prosecutor's comments, details, background, shares)
STOCKHOLM, April 1 (Reuters) - Sweden's Economic Crime Authority said it will not investigate Swedbank over a criminal complaint alleging money laundering brought by campaigning investor Bill Browder.
Swedbank is embroiled in a fast-growing money laundering scandal involving Danske Bank, which revealed last year that its Estonian branch was used to move 230 billion euros ($258 billion) of suspicious payments between 2007 and 2015.
Browder alleged that Swedbank accounts were used to launder $176 million between 2006 and 2012 and this was linked to money laundering and tax fraud exposed by his former lawyer Sergei Magnitsky, who died in a Russian jail in 2009.
Sweden's largest bank, which did not respond to requests for comment on Monday, dismissed its chief executive last week under pressure from already disgruntled shareholders who were spooked by the EBM economic crime agency expanding a separate investigation into Swedbank's conduct.
EBM said its decision did not affect an unrelated probe into whether Swedbank breached insider trading rules by informing major investors about a TV report in February alleging money laundering before it went public. This was broadened last week to include suspected fraud.
The agency said it had dropped Browder's complaint, which was filed last month, as the limited transfers involving Swedish accounts had occurred before tighter anti-money laundering legislation was introduced in 2014 and as a statute of limitations had expired in the case.
"As Swedish prosecutors we have to look at Swedish situation and transactions or persons within our own jurisdiction. That's what we've done and that's why we've decided not to initiate a criminal investigation," Henric Fagher, EBM's Chief Prosecutor in Gothenburg, told Reuters.
Browder, who founded Hermitage Capital and was once the biggest foreign money manager in Russia, has been instrumental in driving authorities to bring cases against Danske Bank.
He was not immediately reachable for comment.
Fagher said he was in contact with and ready to assist a European network of prosecutors as most of the transactions were connected to Baltic states, but declined to say whether any of them were looking at bringing charges.
Swedbank, which is also the target of a four-way probe by regulatory authorities in Sweden, Estonia, Latvia and Lithuania, has lost about a third of its value over worries that it could face lawsuits, fines or sanctions.
Its shares were up 1.6 percent at 133 Swedish crowns at 1023 GMT. ($1 = 0.8899 euros) (Reporting by Esha Vaish, editing by Niklas Pollard, Jane Merriman and Alexander Smith)