"There are extensive operations to gather in money and to finance terror activities which are directed at another country, Turkey," Billström told the Dagens Nyheter newspaper in an interview.
He said that the terror group's fingers extended into gang crime in Sweden, and that Sweden was a base for PKK activities in protection rackets, drug selling and "a whole range of things which damage Swedish society".
"We have only things to gain by cooperating with Turkish authorities when it comes to sharing information and surveillance of organised crime," he said. "But we also have a responsibility towards Turkey to get a hold of this problem."
Turkey's authorities have passed Sweden a long list of mainly Kurdish people living in Sweden who they accuse of being involved in or supporting the PKK, but Sweden's government has insisted that the arrest, trial and sentencing of suspected terrorists is a matter for the criminal justice system.
Billström said, however, that the police had increased their activities in tracking the PKK.
"As a result of the police devoting resources into mapping out the issue it's clear that this is a much bigger problem than we previously thought."
Sweden's government hopes that the new terror law which came into force on June 1st will mark a breakthrough in its crackdown on the PKK.
"This is a question which we have to take seriously it's not something we're doing just to win points in a negotiation," Billström said.
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