“We will insist on establishing control at the borders, although this means that we will possible have to modify the Schengen agreement,” Diaz told El Pais.
Diaz said that such measure is needed in order to limit movement of Islamic militants returning to Europe from the Middle East.
On Wednesday, brothers Cherif and Said Kouachi killed 12 people in an attack on the office of Charlie Hebdo magazine, known for its anti-Islam cartoons. The brothers reportedly claimed allegiance to al-Qaeda in Yemen after the shooting.
The following day, a female police officer was killed during a shootout in Montrouge, a suburb of Paris. The French Prosecutor's Office classified the incident as a terrorist attack.
IS, which has proclaimed a caliphate over the controlled swathes of land in Iraq and Syria, draws fighters from across the globe. According to UN estimates, some 15,000 foreign fighters, including many Europeans, have travelled to Syria to join extremist groups since 2011.