Senior Israeli diplomats are heading to Egypt and the United States as efforts to end the fighting in Gaza are stepped up.
Israeli Foreign Minister Tzipi Livni is bound for Washington, where she will discuss ways of stopping arms being smuggled to Hamas militants, reported SKY news.
At the same time chief Israeli negotiator Amos Gilad will fly to Cairo for more talks on the latest Egyptian ceasefire proposals.
Israel wants Hamas to stop firing rockets into its territory and an arms embargo on Gaza's militant rulers.
Hamas has told Egyptian mediators it would agree to a year-long renewable ceasefire if Israel pulls out all its forces within five to seven days and reopens border crossings immediately, sources said.
In its proposal to Israel, Hamas demanded the opening of all of Gaza's border crossings be guaranteed by Egypt and the international community.
Despite the latest peace moves, the Israeli military is keeping up its offensive in Gaza.
Hamas interior minister Saeed Seyyam was killed in an airstrike which flattened a home in Gaza City.
A top aide, Seyyam's brother and his brother's family were also killed in the attack on a house in the Jabalya refugee camp.
Prime Minister Gordon Brown has meanwhile condemned Israel's shelling of the United Nations HQ in Gaza as "indefensible".
The building was set alight by the bombardment as UN Secretary General Ban Ki-moon visited the area.
Mr Brown has promised Britain will do everything it can to help secure a ceasefire.
He also said UK humanitarian aid would go into Gaza as soon as hostilities stop.
Mr Ban expressed "outrage" over the attack, in which three people were injured.