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.
Police have targeted 17 people in raids in several European countries connected to a suspected jihadist network.