The idea of a truce was floated Sunday by Khaled Meshaal, Hamas' top political leader, based in Syria, during a telephone call to Senegalese President Abdoulaye Wade, who heads the Organization of the Islamic Conference.
Senegal's Foreign Ministry announced that Hamas was interested in a cease-fire if it would include a lifting of Israel's blockade of Gaza, which has severely restricted the flow of goods across the border.
Sentiment for a cease-fire has been growing in Israel among politicians and commentators on the left who supported the air attack but worry that a ground offensive would bog down the army in a costly, unwinnable guerrilla war.
"Israel must constantly check to see when its force has crossed the line of legitimate and effective response," celebrated author David Grossman wrote Tuesday on the front page of Haaretz, advocating a cease-fire.
"Is it possible," he added, "or are we too imprisoned in the familiar ceremony of war?"
France, which holds the presidency of the European Union until Thursday, proposed a 48-hour truce. Israel would halt attacks and lift the blockade to let in humanitarian relief, testing Hamas' willingness to stop the rockets.
If calm prevailed for 48 hours, talks on a long-term cease-fire would begin. The quartet of Middle East peace brokers -- the United States, Russia, the European Union and the United Nations -- called Tuesday for such an accord, and Turkey and Egypt have offered to mediate.
French Foreign Minister Bernard Kouchner twice telephoned Israeli Defense Minister Ehud Barak to discuss France's proposal. Israeli Foreign Minister Tzipi Livni was to meet in Paris on Thursday with French President Nicolas Sarkozy, his office said.
Livni, Barak and Prime Minister Ehud Olmert have refrained from comment on the proposal and kept up their bellicose rhetoric. Israeli media quoted Olmert as saying Tuesday that the aerial phase of the Gaza offensive is just "the first of several" planned.
His spokesman, Mark Regev, said Israel was wary of any proposal "that would give Hamas a respite allowing it to regroup and rearm," as did an Egyptian-brokered cease-fire that took effect in June and broke down last month.
But two other Cabinet officials confirmed Israel's interest in a cease-fire.
"It could be that we would say, 'OK, all right, for humanitarian needs only,' " and we would allow this," Welfare Minister Isaac Herzog told Israel's Army Radio. "Of course this also depends on the other side, where it wants to take this confrontation."