Among those arrested were six suspects in Italy, four in Britain, and three in Norway. Police say some of the suspects may have travelled to Syria or Iraq.
Italy's Ansa news agency said the suspects were accused of international terrorism association.
The network was allegedly plotting to free its leader, Mullah Krekar, who is already in detention in Norway.
Krekar, the Iraqi-Kurdish founder of the radical Islamist group, Ansar al-Islam, is one of those held in the operation.
Two other suspects were arrested in Norway. The three of them are suspected of plotting attacks in Norway and other European countries, according to Italian police.
They face extradition to Italy.
Krekar - born Najm Faraj Ahmad - has served several jail sentences in recent years, including for praising the killing of staff at the French satirical newspaper Charlie Hebdo in January.
The anti-terrorism operation included investigations in the UK, Norway, Finland, Germany and Switzerland, Italian police said.
Arrest warrants were issued for 17 people and at least 13 were arrested.
The detainees are suspected of involvement in a group called Rawti Shax, described as a "terrorist organisation of Kurdish-Sunni origin".
Some suspects could not be located, as they are believed to have travelled to Syria and Iraq to join jihadist organisations, according to the EU's judicial co-operation agency, Eurojust.
Sixteen are Kurdish or Kosovan, according to Ansa news agency.
In a statement, Eurojust said Rawti Shax - or Didi Nwe - represented "an evolution" of Ansar al-Islam, which is listed by the UN as a terrorist organisation affiliated with al-Qaeda.
According to the Italian investigation, it was founded in Europe, with cells operating via the internet.

Former actor John Denham, 49, said conversations he had had about it were "fantasy" and he did not think "any of that stuff" would happen.
Mr Denham, from Wiltshire, has pleaded guilty to child pornography offences and conspiracy to engage in sexual activity in the presence of a child.
He and co-accused Matthew Stansfield, 34, deny conspiracy to rape a child.
They also deny conspiracy to sexually assault a child under the age of 13.
Mr Stansfield, from Hampshire, has pleaded guilty to child pornography offences.
The court heard that the alleged plan to rape a baby was to have taken place on 17 January last year in Bedfordshire.
However, it did not happen because another man, Robin Hollyson, who had access to the intended victim, had been detained in hospital.
Hollyson, 30, has already pleaded guilty to the rape of a child and conspiracy to rape a child during 2013 and 2014.
Mr Denham, who has two children and was previously known as Benjamin Harrop, said in court he did not believe the intended victim existed.
But he admitted that months afterwards he had watched a video showing Hollyson raping the child.
The court has heard how members of a gang raped and abused young children, live streaming the attacks over the internet.
The men contacted each other using Skype, video conferencing software and online chatrooms.
Mr Denham said he had begun by viewing adult pornography online but after seeing an image of a young teenage girl performing a sex act on a man he became "oddly fascinated" by child pornography.
He said he became "desensitised" to what he was seeing on screen and the age range "dropped lower and lower".
He said he was "ashamed" of deriving sexual gratification from child pornography and now understood there were "real victims".
"It wasn't reality for me at the time," he said.
"When I wasn't online and when I was in the real world I viewed children as they should be viewed. I didn't look at them in a sexual way at all."
The trial continues.
Police have targeted 17 people in raids in several European countries connected to a suspected jihadist network.
[NEXT_CONCEPT]
A paedophile accused of conspiring to rape a baby has told a court in Bristol the alleged plan was "pie in the sky".