The man was arrested in Berlin on Saturday on suspicion of supporting a "terrorist organisation", but prosecutors have decided not to seek an arrest warrant to keep him in custody, Hartmut Schneider, spokesman for the federal prosecutor's office said on Sunday.
He gave no further details.
A judge in Karlsruhe on Saturday issued a formal arrest warrant for three other men who are accused of belonging to Ansar al-Islam, a group that has mounted attacks on US and allied forces in Iraq since last year's invasion.
They were taken into custody on Friday on suspicion of planning an attack on Allawi, hours before he met Chancellor Gerhard Schroeder.
Prosecutors did not release the suspects' names.
Before Allawi's visit, investigators who had the three suspects under surveillance noticed an increase in activity, phone calls and suspicious movements that amounted to evidence of plans to attack, prosecutors said.
Ansar al-Islam, which was formed in the Kurdish parts of Iraq, is said to include Arab al-Qaida members who fled the US-led invasion of Afghanistan in late 2001.