Arab countries called an emergency session of the U.N. Security Council on Wednesday to debate the violence in Gaza, demanding in a draft resolution an immediate ceasefire between Israel and Palestinian militants.
The evening session adjourned without a vote being called and diplomats said negotiations would be held in coming days over the draft.
Western delegates described it as unbalanced and focusing almost entirely on Israel's actions.
The resolution, presented by Libya, called for "an immediate ceasefire and for its full respect by both sides." It also demanded protection for Palestinian civilians, opening border crossings into Gaza and "restoration of calm in full."
The council has already issued a statement, which lacks the weight of a resolution, calling for a halt to the violence in Gaza, but it has been ignored.
The United States says any ceasefire must be durable and binding on the Hamas Islamists who control Gaza, as well as on Israel.
Israel, which began air strikes on Gaza on Saturday to try to stamp out the Palestinian rocket fire, has rejected calls for an immediate ceasefire.
Nearly 400 Palestinians and four Israelis have been killed.
Foreign pressure has grown on both sides to end hostilities, but Israel brushed aside as "unrealistic" a French proposal for a 48-hour truce that would allow in more humanitarian aid for Gaza's 1.5 million residents.
"If conditions will ripen and we think there will be a diplomatic solution that will ensure a better security reality in the south, we will consider it. But at the moment, it's not there," an aide quoted Mr Olmert as saying.
"We didn't start this operation just to end it with rocket fire continuing as it did before it began," Mr Olmert said, according to the aide.
Mr Olmert made the remarks, which did not rule out a ceasefire in the future, to his security cabinet.
Hamas said it was prepared to study proposals for a ceasefire so long as it "will bring an immediate cessation to the aggression and lift the siege entirely," senior official Ayman Taha said, referring to Israel's blockade of the Hamas-ruled coastal territory.
With Palestinians increasingly enraged over the offensive, President Mahmoud Abbas called for the fighting to be stopped "immediately and without any conditions" and said Israel was "fully responsible" for the carnage.
Along the heavily-fortified border fence, Israeli tank crews prepared for battle while Islamist militants, hiding as little as a few hundred metres away, laid land mines and other booby traps should a ground war break out.