"The head of the Ezzedine al-Qassam Brigades Abu Khaled is still alive and leading the military operation," a source close to the Islamist movement told AFP, using Deif's nom-de-guerre.
His remarks were made after an Israeli air strike levelled a six-storey house in Gaza City, killing Deif's wife and infant son.
It was not immediately clear whether Deif had also been killed or injured in the strike, which also killed another woman and a teenager.
Hamas spokesman Sami Abu Zuhri also issued a statement, saying Israelis would not be safe until Deif decided so.
"The occupation will pay for its crimes against Palestinian civilians and those living around the Gaza border will not return home until Mohammed Deif decides so," he said.
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Earlier, Israel's Foreign Minister Avigdor Lieberman called for military action to topple Hamas, saying the Islamist movement was clearly dictating the pace of the confrontation.
"This policy of 'quiet for quiet' effectively means that Hamas is the initiator and the one deciding when, where and how to shoot at Israeli citizens," he wrote on his Facebook page.
"Hamas is controlling the height of the flames and choses when to disturb the rhythm of life for people in Israel," he said, indicating the rocket fire from Gaza was unlikely to stop.
"When we speak seriously about Israelis' security we must understand that there is no other option other than decisive action with one meaning - toppling Hamas."
Lieberman is one of the most hardline members of Israel's inner security cabinet, which was meeting on Wednesday afternoon to discuss the situation, media reports said.