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.
The ministers are to hold talks with Ban Ki-moon, the UN secretary-general.
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, remains on the table.
Mahmoud Abbas, the Palestinian president, is expected to arrive in New York on Tuesday and is hoping the council will adopt the resolution.
However, the US called it "unacceptable" and "unbalanced" because it didnt 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.