"It seems the plan was going into a closing phase," police spokesman Joern Bro said on Friday.
The men, all Danish Muslims aged between 16 and 20, were arrested on Thursday morning.
At a court hearing late on Thursday they were ordered held in jail until 16 November as police continue the investigation, Bro said.
He declined to give details, saying only that the network had planned to carry out the attack in Europe.
Danish media quoted Bro as saying that the arrests in Copenhagen were linked to an investigation in the Balkans in which arrests were made and large quantities of explosives were found on 19 October.
He did not specify where the Balkan investigation took place but Bosnian police last week said they arrested three people - a Turkish, Swedish and Bosnian national - in Sarajevo on suspicion of preparing terrorist activities.
Denmark has 500 soldiers
supporting the US in Iraq
Police said they found explosives, firearms and other military equipment in connection with those arrests on 19 and 20 October.
According to Sarajevo's Dnevni Avaz daily newspaper, one of the three suspects was an 18-year-old who was preparing a bomb attack on the Sarajevo embassy of a European Union country.
The Danish suspects, who were not identified, were ordered detained at a court hearing in Glostrup, a suburb of Copenhagen.
Police said they raided the suspects' homes in Copenhagen and suburbs of the capital, seizing computers, computer discs, books with radical Muslim literature and mobile phones. Police also found 200,000 kroner ($32,400) in cash.
Some 25 people in all were briefly detained but only four were arrested.
Denmark has not been hit by terrorism in two decades, but fears have grown the Scandinavian country could face an attack after the July attacks on the London transit system.
Like Britain, Denmark contributes to the US-led forces in Iraq and has about 500 soldiers stationed there.
In the weeks after the bombings that killed 56 people in London, Danish police stepped up patrols at train and subway stations.