The US insists that the Israeli blockade of Gaza is a form of self-defence in the face of rockets fired from the Palestinian territory.
However, Riyad Mansour, the permanent Palestinian observer to the UN, said that the situation was "absolutely untenable".
He said: "The Israeli policy of brinkmanship is creating a humanitarian catastrophe in the Gaza Strip, heightening fears and tensions, inciting, provoking and fueling the vicious and dreaded cycle of violence."
Bashar Jaafari, the Syrian ambassador to the UN, accused the US of politicising the Gaza siege.
"The language of the presidential statement as written reflects only the humanitarian aspect of the situation in Gaza," he said.
"The American position is based on politicising it by adding new elements in it."
The Security Council is to meet again on Thursday to try to reach a consensus.
Arab ambassadors have said that if Washington blocks the adoption of the latest non-binding text, they could push for a resolution rather than a statement.
Or they might take their case to the 192-member General Assembly, where they are confident of securing support.
The latest version of the draft expresses "deep concern about the steep deterioration of the humanitarian situation" in Gaza.
It "calls on all parties to immediately cease all acts of violence, including the firing of rockets into Israeli territory and all activities which are contrary to international law and endanger civilians", a reference to the Israeli siege.