President Bush has blamed the violence in Gaza and southern Israel firmly on Hamas, after a week of Israeli air strikes and Palestinian rocket attacks, BBC reported.
Mr Bush, who has just weeks left in office, said Hamas was a terrorist group dedicated to destroying Israel.
Earlier the Hamas leader-in-exile, Khaled Meshaal, warned Israel of a "black destiny" if it began a threatened ground offensive on Gaza.
Hamas said one of its military leaders died in an overnight strike.
Abu Zakaria al-Jamal died of his wounds after a raid.
Israel has now carried out more than 700 strikes on Gaza since launching the offensive last Saturday, AFP news agency said.
The UN warned of a worsening humanitarian crisis in Gaza.
The UN said it believed 25% of more than 400 Palestinians killed by Israeli action so far were civilians.