In Paris, Ashcroft may face some opposition
Mr Ashcroft is due to visit London, Madrid, Berlin, Brussels and Rome before returning to Washington on Sunday.
His delegation will include several senior FBI officials, lawyers and judges.
Several suspects linked to the attacks remain in European custody, including a Moroccan suspect, Mounir al-Motassedeq, who is alleged to have shared a Hamburg apartment with two of the hijackers.
In Spain, eight al-Qaeda members were arrested and others are currently in custody in France, Belgium and Italy.
However some European authorities, including French President Jacques Chirac, have expressed concern about extraditing suspects to the United States for trial.
They are reluctant to send suspects for trial in a country where they may face execution if convicted.
Methods criticised
Mr Ashcroft has frequently been criticized for his methods in fighting the war against terror, both by European observers and by those in his country.
In particular, plans to conduct the trials of terrorism suspects under military jurisdiction have come under fire from civil liberties groups.
Military trials require only a two-thirds majority to secure a guilty conviction, as opposed to the unanimous verdict needed by civilian courts.
And legislation permitting the FBI to listen in on attorney-client conversations has also been criticised as being against the US Constitution.
The US is currently holding 623 people in detention; however, none as of yet have been proved to have links with Osama Bin Laden's al-Qaeda network.
It also proposes to question a further 5,000 Middle Eastern men regarding the attacks, most of whom entered the United States on student or tourist visas.
Immigration relief
In addition, Mr Ashcroft announced towards the end of November that illegal immigrants who offered information on the terrorist attacks would be offered visas and citizenship.
Those coming forward to US authorities with specific intelligence on the attacks in America would be offered "immigration relief" - in some cases permission to stay legally in the US.
"The people who have the courage to make the right choice deserve to be welcomed as guests into our country and perhaps to one day become fellow citizens," he said at the time.