Israel's cabinet was discussing a temporary truce as the death toll in its bombardment of Gaza passed 100, prompting further international concern.
European leaders urged Israel to hold fire immediately, while the UN also pressured both sides to accept an Egyptian offer under which a 24- or 48-hour ceasefire would be declared to allow a fully fledged deal to be worked out.
There were indications that this had been accepted by Hamas, while Israel appeared undecided.
"We are moving now with the Palestinians into a T-junction," said Major General Dan Harel, a former vice-chief of the Israeli defence staff.
"Since the Palestinians keep shooting into Israel, there are only two ways out. One is through a ceasefire agreement cooked in Cairo. The other is escalating the situation with a land effort, which is going to be very bad for both sides. We are 24 to 48 hours from that junction."
Western backing for Israel has become strained in the face of civilian casualties, including the loss of four children and five women from one family in an air strike on Sunday. The death toll from Israeli strikes includes 53 civilians, according to local health officials.
They said 840 people, including 225 children, had also been wounded. Three Israelis have been killed.
A statement agreed by EU foreign ministers condemned civilian losses on both sides and reiterated Israel's "right to defend itself".
But it urged Israel "to act proportionately and ensure the protection of civilians at all times", adding that there was an "urgent need to move towards a two-state solution".
Ban Ki-moon, the UN secretary-general, arrived in Cairo for talks and will travel to Jerusalem today.
An Egyptian official close to the negotiations hosted by Cairo said "signals" for a ceasefire were good.
If there is to be a ceasefire, it would be unlikely to meet the either side's terms. Hamas is demanding a lifting of the blockade at its borders.
Israel wants a long-term end to attacks from Gaza, and guarantees from Egypt that Hamas will not be allowed to rearm through the Sinai desert.
The Egyptian official said that Cairo was trying to persuade both sides to accept a ceasefire with fewer conditions, leaving details of a truce to be worked out afterwards.
"Israel has to calculate very carefully before the transforming relationships around us: it is now about how to find the right exit point, which won't be too early or too late," said Brigadier General Mike Hertzog, former chief of staff to the Israeli defence minister.
There was no let-up in the fighting yesterday. A senior figure from Islamic Jihad was among 24 Palestinians killed when a missile struck an apartment block containing international media offices.
Rocket fire from Gaza into Israel was heavier than Sunday but intermittent. Last night's estimate of the number of rockets fired was 91. (© Daily Telegraph, London)