The latest targets included three government buildings in Gaza City, struck by Israeli missiles in the early hours of Thursday local time.
Palestinian officials said the attacks left at least 25 people injured.
The special session of the security council followed calls from Arab countries for an urgent resolution demanding an immediate ceasefire, and warnings from aid agencies that the people of Gaza are facing a humanitarian catastrophe.
But diplomats said the meeting was unlikely to produce any vote in the near future, with deep divisions among council members over the wording of any resolution.
Negotiations are expected to continue in the coming days.
But despite mounting international pressure, Israel has so far rejected calls for a ceasefire and has continued to build up its forces along the border in preparation for a possible ground invasion.
It says the assault is aimed at the Hamas leadership in Gaza and intended to destroy the ability of its fighters to launch rocket attacks on Israeli towns and cities.
During Wednesday's Security Council meeting, Libya, the only Arab country on the council, presented an Arab-drafted resolution calling for "an immediate ceasefire and for its full respect by both sides."
But diplomats said the wording of the draft was unlikely to be acceptable to the veto-holding United States and other Western countries.
"It's going to need a lot of work," one Western diplomat told Reuters.
The draft resolution, a copy of which was obtained by Al Jazeera, denounced "the excessive, disproportionate and indiscriminate use of force by Israel" but made only vague reference to Hamas rocket attacks on Israel.
The US has said any lasting ceasefire is dependent on concrete assurances from Hamas – in terms that are acceptable to Israel – that the rocket attacks will stop.
With food and fuel supplies running dangerously low, the situation for thousands of Gaza residents is becoming increasingly desperate.
According to John Holmes, the United Nation's chief humanitarian official, more than 20,000 people have gone without food since the beginning of the Israeli assault, with many more resorting to begging or picking through rubbish dumps.
During Wednesday's UN meeting Riyad Mansour, the Palestinian permanent observer, called on the Security Council to take strong and urgent action.
"Our children in the Gaza Strip today and their mothers are looking up to you to stop this barbarian aggression and to protect them from this criminality, this forced hunger and this deliberate killing," he said.
"We hope that you will not let them down."
|Thousands of Gaza civilians have little or no shelter from Israeli raids [AFP]
Earlier on Wednesday in a strongly-worded statement, Mahmoud Abbas, the Palestinian president, threatened to abandon peace talks in response to what he called Israel's "criminal aggression".
"The most important obligation is to rally the forces, nationally and regionally, to end the barbaric and criminal Israeli aggression against our people in the Gaza Strip," he said in a televised address.
At least 393 Palestinians, including dozens of civilians, have been killed and about 1,600 injured as Israeli warplanes and helicopter gunships have dropped hundreds of bombs and missiles on the densely-populated strip.
Abbas, who had been criticised for blaming rival faction Hamas for provoking the Israeli attacks, and accused of colluding with Israel over the operations on Gaza, said he "would not hesitate to put negotiations to an end if they come into conflict with our interests".
"Peace does not mean humiliation or surrender," he said. "Our people are still equipped with more options."
His statement followed comments from Ehud Olmert, the Israeli prime minister, who said: "If conditions 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."
"Israel will embark on a veritable adventure if it decides to invade Gaza. We have prepared surprises for them"
senior Hamas official
Olmert was speaking after Israel's security cabinet rejected a French proposal for a 48-hour truce to allow for the passage of humanitarian aid into the besieged territory.
Mark Regev, an Israeli government spokesman, said a "durable" solution was needed rather than the "band-aid" that would be provided by a 48-hour truce.
"What we need is a solution that will create real quiet ... the only people who really wanted this were Hamas, because we have been hitting them hard and they'd like time to regroup and rearm," he told Al Jazeera.
Israel has targeted many of the underground tunnels leading out of Gaza into Egypt, which have been a lifeline to Palestinians for food, fuel and medical supplies since Israel closed Gaza's border crossings 18 months ago.
|Israeli forces have massed along Gaza's border ahead of a possible invasion [GALLO/GETTY]
In addition Israel's military has been moving soldiers, tanks and armoured personnel carriers to Gaza's edge amid ongoing concerns that the aerial assault will be followed by a ground offensive.
Hamas said on Wednesday that it would fight "until the last breath" if Israel sent ground forces into Gaza.
"Israel will embark on a veritable adventure if it decides to invade Gaza. We have prepared surprises for them," Mushir al-Masri, a senior Hamas official, said.
Ayman Mohyeldin, Al Jazeera's correspondent in Gaza, said that in the event of a ground incursion, Palestinian factions felt that they had the advantage, due to the preparations they have made over the past six months of the truce.
"They say they have acquired new weapons, new munitions, new explosive devices and this is where they feel they enjoy more of an advantage in terms of the ability to face an Israeli incursion," he said.
"They certainly know they can't compete with Israel's air superiority and that is why Israel has been warned against launching a [ground] operation here in Gaza."