"If Hamas does not soon release Israeli hostages in Gaza ... and stops shooting rockets at Israeli communities, they will meet attacks of a kind not seen in Gaza for a long time", said Katz in a statement after visiting the Israeli city of Netivot.
At least twelve people have been killed in Israeli attacks in Gaza on New Year's Day. Most of the victims were women and children, according to the authorities in Gaza.
In one of the attacks, a house in northern Gaza was hit. Seven people, including one woman and four children, were killed, according to the authorities.
In another attack, the al-Bureij refugee camp was reportedly hit, where a woman and a child died. The Israeli military says it responded to rocket fire from al-Bureij and ordered an evacuation before launching the attack.
In the city of Khan Younis in the south, three people were killed, according to hospital sources.