UN sources said the proposed new resolution would have three main points: An urging for an immediate ceasefire, the formation of some sort of "humanitarian corridor" for much-needed aid and a form of "monitoring mechanism" for the ceasefire.
Jean-Maurice Ripert, French ambassador to the UN said after the discussions: "We will do our best to have a resolution as soon as possible, and as soon as feasible."
However Gabriela Shalev, Israel's UN ambassador said there was no point any ceasefire resolution while Hamas fighters continued to fire rockets at Israel.
"The situation will be ripe for a ceasefire whenever Hamas will stop shooting the rockets and we will have guarantees that there is going to be a comprehensive package to ensure a long-term ceasefire," she told Reuters news agency.
Further informal talks between council members are expected to continue on Tuesday morning, while later on in the day Mahmoud Abbas, the Palestinian president, will also arrive in New York for talks with the UN secretary-general.
An open meeting is also reported to be held on Tuesday where Abbas will address the council.
Ahead of the meeting Riad Malki, the Palestinian foreign minister, said the meeting was to "show harmony among Arabs" and support for a speedy end to the Israeli offensive.
Malki said he hoped the Security Council would pass a resolution calling for an "immediate and permanent" ceasefire in Gaza.
Malki said the Arabs wanted "a resolution that will permit first of all ending the Israeli aggression against the Palestinian people in Gaza and calling for an immediate and permanent ceasefire, lifting the siege, opening the crossings between Gaza and Israel, and also between Gaza and Egypt".
At least 548 Palestinians have been killed in Gaza in the last 10 days, with more than 80 deaths reported since Israeli launched a ground offensive that began on Saturday.
In a statement released on Sunday, Ban appealed "to all members of the international community to display the unity and commitment required to bring this escalating crisis to an end".
An Arab draft resolution circulated by Libya last week, condemning Israel and calling for an end to its offensive, was dismissed by the US as "unacceptable" and "unbalanced" because it did not call for an end to Hamas rocketfire targeting Israel.
On Monday, George Bush, the US president, said any ceasefire to end the Gaza crisis must include provisions that prevent Hamas from using the coastal strip to fire rockets into Israel.
"Instead of caring about the people of Gaza, Hamas decided to use Gaza to use rockets to kill innocent Israelis," Bush said at the White House.
"Any ceasefire must have the conditions in it so that Hamas does not use Gaza as a place from which to launch rockets," Bush added.