He spoke as mediators continued efforts to salvage the Gaza Strip ceasefire deal shattered by Israel's renewal of air and ground war on March 18 after it and Hamas failed to agree on terms for an extension of the two-month-old truce.
Israel has said it will never again accept Hamas governance and military power in the enclave following the militants' October 7, 2023 cross-border attack that led to the Gaza Strip war.
The Israeli military said last week that its forces had begun a focused ground operation in the central and southern Gaza Strip after it resumed bombardments in the besieged enclave that have killed hundreds of Palestinians.
Israeli Prime Minister Benjamin Netanyahu has said the objective of the new campaign is to force the Islamist militants to release remaining hostages.
"If Hamas continues with its intransigence, it will pay heavy prices that get higher and higher in the taking of territory (by Israel) and in taking out militants and terror infrastructure until its complete surrender," Katz said in a video reported by Israeli media.
The latest offensive has been among the deadliest since the conflict began 17 months ago, splintering a shaky ceasefire that had largely prevailed since it went into effect on January 19.
Hamas is still holding 59 hostages, with 24 thought to be still alive, among the more than 250 it seized in its October 7, 2023 attack on Israel.Â
Most of the rest have been freed, or their bodies handed over, in negotiated exchanges.
Israel's subsequent military assault on the Gaza Strip has killed more than 50,000 Palestinians, according to the Hamas-run health ministry.
