A fourth man is also reported to have been taken into detention.
The investigating magistrate in the southwestern town of Karlsruhe was to decide on Saturday whether to hold the three men in custody. They were arrested on Friday after early morning raids in three German cities.
"The three are under unprecedented security measures as they are hand-cuffed and chained at the legs and have been transferred by helicopters to appear before the German examining magistrate at the German Supreme Court," said
Aktham Sulayman, Aljazeera correspondent in Berlin.
"There is a possibility the magistrate might keep them in prison under examination," he added.
The suspects, believed to be members of the armed group Ansar al-Islam, are accused of planning an attack during Allawi's visit to Germany this week.
The prosecutor's office said the fourth man, a Lebanese, was arrested on Saturday in Berlin on suspicion of supporting Ansar al-Islam, described as a foreign terrorist organisation, adding that his home was searched.
The other three had been picked up in Berlin, Stuttgart and Augsburg.
The Karlsruhe prosecutor said it was still unclear whether the fourth man would also be charged.
Ansar al-Islam is an armed group originating in Kurdish-held northern Iraq. Prosecutors have been investigating its activities in Germany, which authorities say included fund-raising, trafficking and propaganda, since December 2003.
The United States accuses it of working closely with al-Qaida and with the network of Abu Musab al-Zarqawi, the most prominent leader of fighting in Iraq.