Ammunition and weapons were found in a connected search, the police later tweeted.
“The arrests took place as part of efforts to combat people enlisting in terrorist groups in the war-torn areas in Syria and northern Iraq,” the police said in a statement on Thursday.
The police would not provide more details on the identity of or suspicions about the four, who will come before a judge for a preliminary hearing on Friday.
“The suspects have been identified through investigations carried out in close cooperation between the Danish Security and Intelligence Service and Copenhagen police,” the statement said.
Under Danish terrorism law, “letting oneself be recruited to commit acts of (terrorism)” is punishable with up to six years in jail.
“At one of the addresses we (searched) today we found some weapons and ammunition,” police inspector Poul Kjeldsen told reporters.
A person living at the address had links to one of Copenhagen’s criminal gangs, police later said on Twitter.
A preliminary hearing was scheduled to be held on Friday.
More than 125 people from Denmark have are believed to have joined ISIS after going to Syria and Iraq, Danish intelligence service PET, said in October, adding that at least 27 of them have died there.
“We know that people who have fought for ISIS in Syria or Iraq may pose a specific security threat against Denmark,” Justice Minister Soren Pind said in statement shortly after the arrests.
Danish authorities have been on high alert since two people were killed in shooting attacks on a free speech event and a synagogue in Copenhagen in February last year.
Europe is on edge after the Paris attacks in November and last month’s bombings in Brussels, both blamed on homegrown militants radicalized and trained by ISIS.
ISIS has claimed responsibility for bombing that killed 32 people in Brussels last month and attacks in Paris on November that killed 130 people.
Around 4,000 Europeans have travelled to Syria and Iraq to join extremist groups as foreign fighters, according to a study from the Hague-based International Centre for Counter-Terrorism released last week.
Data from Denmark showed that 125 people had left the country to fight in Syria or Iraq, and that 62 of those were believed to have returned to the Scandinavian country.
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