Mofaz, one of Israel's deputy prime ministers and a member of the main coalition party Kadima, ruled out direct political negotiations with the Islamic movement unless it recognises Israel.
"If Hamas comes to us with a serious proposal for a long-term truce, in my opinion Israel should not reject it. For that, it would not be vital for Hamas to recognise Israel first," Benjamin Ben-Eliezer, Israel's infrastructure minister, said on Friday.
"What is essential is that it stops rocket fire and all other attacks against Israel from Gaza, and that it agrees to stop arms smuggling on the Egypt border," Ben-Eliezer said.
"Making recognition of Israel a precursor to negotiations would be the best way of torpedoing it from the beginning," he said.
Ben-Eliezer linked dialogue with Hamas to the release of an Israeli soldier captured in June 2006 by Palestinian fighters on the Gaza border.
Hamas seized control of the Gaza Strip in mid-June.
In his opinion, Hamas was "showing signs of weariness" because of Israeli military operations in the Gaza Strip and economic sanctions.
But the office of Ehud Olmert, Israel's prime minister, denied that Israel was considering a ceasefire proposal from Hamas, blacklisted as a terrorist group.
"Israel talks to the Palestinian Authority [lead by Mahmud Abbas, the Palestinian president] and not with extremists," a government official said.
"We will not let terrorist organisations continue to strike or regroup. We will continue to employ all necessary means to stop them from attacking our towns," the official said.
Israeli air strikes and ground operations in the Gaza Strip have killed 20 Palestinian fighters from different armed groups since Tuesday