Israeli leaders met late into the night to discuss Egyptian proposals to end the violence.
Further talks are expected to take place in Cairo on today.
More than 100 people have died in the Gaza strip since the Israel bombardment began and at least three Israelis have been killed by rockets fired by Palestinian militants.
However, Israeli officials are quoted as saying that any possible ground invasion of Gaza has been put on hold while the ceasefire talks continue.
Israeli Prime Minister Benjamin Netanyahu and his top ministers debated their next moves in a meeting that lasted into the early hours of Tuesday.
“Before deciding on a ground invasion, the prime minister intends to exhaust the diplomatic move in order to see if a long-term ceasefire can be achieved,” a senior Israeli official, speaking on condition of anonymity, said after the meeting.
Any diplomatic solution may pass through Egypt, Gaza’s other neighbor and the biggest Arab nation, where the ousting of U.S. Ally Hosni Mubarak and election of President Mohamed Mursi is part of a dramatic reshaping of the Middle East, wrought by the Arab Spring and now affecting the Israeli-Palestinian conflict.
Mursi, whose Muslim Brotherhood was mentor to the founders of Hamas, took a call from Obama on Monday telling him the group must stop rocket fire into Israel – effectively endorsing Israel’s stated aim in launching the offensive last week. Obama, as quoted by the White House, also said he regretted civilian deaths – which have been predominantly among the Palestinians.
“The two leaders discussed ways to de-escalate the situation in Gaza, and President Obama underscored the necessity of Hamas ending rocket fire into Israel,” the White House said.
“President Obama then called Prime Minister Netanyahu of Israel and received an update on the situation in Gaza and Israel. In both calls, President Obama expressed regret for the loss of Israeli and Palestinian civilian lives.”
Three Israeli civilians and 108 Palestinians have been killed. Gaza officials say more than half of those killed in the enclave were civilians, 27 of them children.