Three men fighting extradition from the UK are alleged to have been key members of a terror group that planned to kidnap a British ambassador.
Bakr Hamad, 38, Zana Rahim, 32, and Awat Hamasalih, 33, held senior positions in Rawti Shax, Westminster Magistrates' Court was told.
The group plotted to carry out attacks across Europe, it is alleged.
The men were arrested in the UK last week following an international counter-terrorism operation.
They were among 13 people taken into custody after raids in six European countries following an international counter-terrorism operation.
The three men, all Iraqi nationals, face extradition to Italy where they are accused of conspiring to commit international terrorism and subvert democracy.
The arrests were made at the request of Italian authorities.
Daniel Sternberg, representing Italian authorities, told the London court hearing the arrests were made to dismantle a Europe-wide jihadist network.
Rawti Shax aimed to carry out attacks on Western and European targets, he added.
Mr Sternberg said: "The organisation aimed to establish caliphate in Iraqi Kurdistan and sought to establish cells in Europe to share and disseminate jihadi material and to participate in jihad in Iraq and Syria together with Islamic State and Al Nusra."
When Rawti Shax's leader Mullah Krekar was arrested and jailed in Norway in 2012, the group drew up plans to kidnap dignitaries - including a British ambassador - to barter for his release, it is alleged.
It is also claimed the group planned to smuggle missiles into Norway to commit jihad.
Hamad, of All Saints Street, Kingston-upon-Hull, Rahim, of Curzon Street, Derby, and Hamasalih, of Finchley Road, Birmingham, all denied consent for extradition at an earlier hearing.
Their lawyers said they would be challenging extradition on the grounds of "refoulment", the illegal returning of refugees. They may also invoke Article Two (right to life) and Article Three (prohibition of torture) of the European Convention on Human Rights.
A fourth man arrested in Britain has been told he no longer faces action.
Sharif Kadir, 52, of Gleadless Road, Sheffield, appeared ahead of the extradition hearing, when the court was told the European arrest warrant for him had been withdrawn. He remains in immigration detention.