Hamas' Izz ad-Din al-Qassam Brigades blamed the Israeli "occupation" for the "atrocious" explosions aimed at police officers in Gaza city last Tuesday.
Hamas emphasized that they will not allow more attacks such as these, and they will prevent attempts to disrupt stability.
Both of the suicide bombings on Tuesday were carried out by extremist Islamic activists, and three Gazan police officers were killed.
In a Friday announcement, the Izz ad-Din al-Qassam Brigades demanded the Interior Ministry, which is responsible for security, speed up the investigation of the attacks. They also demanded authorities apply the harshest punishments to anyone who participated in planning and carrying out the attacks.
In addition, they claimed that those responsible for the attacks sold their souls to the enemy and its collaborators in their attempts to disrupt security and stability on Gaza's internal front.