EU anti-terror chief Gilles de Kerchove on Tuesday called for a boosted exchange of information with Tunisia, which has seen its nationals involved in deadly attacks abroad and on its soil.
During a visit to Tunis, for talks with Tunisian ministers, the EU official said that the flow of information across the Mediterranean "is functioning well" but could be improved.
"We are looking to see how to help Tunisia in the area of data protection... to increase the exchange of information," between the Tunisian authorities and organisations such as Europol and Eurojust, he added.
He argued such improvements could be useful for ongoing cases like the trial of the suspects in the 2015 attack on a beach resort near Sousse that killed nearly 40 foreign holidaymakers, most of them British.
Families of French and British victims of that attack and one at the National Bardo Museum in Tunis the same year, in which 22 people died, have complained they were not informed of the legal proceedings which followed.
Tunisians have also carried out deadly attacks in Europe, including Berlin and the French towns of Nice and Marseille.
Asked about the arrival in Europe of Ahmed Hanachi, a Tunisian national who killed two women in the southern French city of Marseille on October 1, de Kerchove underlined the difficulty in "identifying the point of changeover from radicalism to violent radicalism".
Hanachi, 29, fatally stabbed the two women at Marseille's Saint-Charles train station before being shot dead by police.
The attack was claimed by the Islamic State group, but French investigators have not found any evidence linking it to the jihadists.
But Hanachi was known to the police for drug as well as alcohol problems and had a history of petty crime, using seven aliases.
"One of the main subjects is to become more and more precise in the detection of the tipping point," the EU commissioner told a press conference in Tunis.