Senior commander Abu Zakaria al-Jemal was killed. He was one of the leaders of Hamas' military wing.
Other targets in Gaza were again bombed by Israeli planes during the night.
Israeli tanks are waiting on the border for the order to go in.
But Hamas political leader, Khaled Mashaal, has warned Israel against a ground offensive. He said a grim fate awaited its troops in Gaza.
Mashaal, who is based in Damascus, said a black destiny awaits Israeli forces if they invade the Gaza Strip.
He said Hamas is ready to cooperate with efforts to end the violence, but will not give in to Israel's conditions.
"Here in a clear expression is our stance. We're ready to cooperate with any genuine attempt that is made to end the aggression against Gaza, to lift the blockade on it and to guarantee the opening of all the crossings," he said.
"However, all those who make moves to help us must know that we will not surrender to the conditions of the Israeli occupation."
It was his first public address since the start of the Israeli bombardment and was a carefully crafted speech aimed at the Israelis, as well as the Palestinians and the wider Muslim world.
The televised speech was broadcast on the Arab satellite channel Al-Jazeera, which reaches millions of people across the Arabic speaking world in the Middle East and beyond.
He said this was not a battle against Hamas alone but against the entire Ummah, or Muslim nation - an apparent reference to a populist Islamist idea that the Palestinians are defending the Muslim world against a modern form of crusades.
Meanwhile, the United Nations (UN) said the people of Gaza are living in a state of fear and panic.
Over 435 people have been killed during the eight days of Israeli onslaught on Gaza, many of them not connected to Hamas.
In Israel there is increasing speculation that tanks will go into Gaza soon - the latest stage of an operation which seeks to uproot Palestinians living in Gaza Strip.
It has been dropping leaflets warning Gazans to leave areas that might be attacked.
Israel says there is no humanitarian crisis in Gaza, but the UN says there is and that it is serious. Eighty per cent of people live on food aid and running water and power are barely functioning.