The group allegedly planned to kill Mr Allawi in Berlin
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The trial has opened in Stuttgart, Germany, of three Iraqi men accused of plotting to kill then Iraqi PM Iyad Allawi on a trip there in 2004.
Prosecutors say the men are members of the radical Ansar al-Islam group with links to al-Qaeda.
Police say they intercepted a phone call between the men agreeing to carry out the attack when Mr Allawi appeared at a business forum in central Berlin.
The men face a maximum jail term of 10 years if found guilty.
Ata Abdoulaziz Rashid, 32, Mazen Ali Hussein, 24, and Rafik Mohamad Yousef, 31, are charged with conspiracy and membership of Ansar al-Islam.
Their case is being heard in a high-security court specially designed for trials of Germany's militant Red Army Faction in the 1970s.
They are being tried under a new law, introduced after the 9/11 attacks, that enables foreign militant groups operating in Germany to face similar punishments to domestic groups.
Pre-dawn raids
Police say Rafik Mohamad Yousef had made a phone call to the other defendants, described as more senior group members.
They say Mr Yousuf was then given approval for the attack and a pledge of financial help.
Mr Yousuf then allegedly inspected the site of the planned attack - a Deutsche Bank building in the German capital - on 2 December 2004, a day ahead of Mr Allawi's visit.
Police then arrested the three in pre-dawn raids.
Mr Rashid and Mr Hussein are also charged with transferring funds to Iraq and Iran on behalf of Ansar al-Islam.
Lawyers for the men complained on the opening day of the trial that they had been searched before entering the court - a practice from which they are normally excluded.
"This stigmatises the defence," lawyer Gul Pinar is quoted by the AFP news agency as saying.
Mr Allawi headed the Iraq interim government in June 2004 and stepped down in April 2005.
Separately, two Iraqi men in the German city of Munich have gone on trial on charges of providing logistical and financial support for Ansar al-Islam.
In January, an Ansar al-Islam member was jailed for seven years in Munich for recruiting fighters and raising funds.