The US has called for restraint by all parties following an Israeli air strike on Syria in the wake of a Palestinian suicide attack in Israel.
Most council members have condemned the Haifa blast
President George W Bush telephoned Israeli Prime Minister Ariel Sharon after the raid underlining the need to "avoid heightened tension in the region at this time," said Ken Lesius, a White House spokesman.
The message was reinforced by US ambassador to the United Nations John Negroponte at an emergency meeting of the Security Council which Syria had demanded to condemn Israel.
Mr Negroponte called on all sides to think carefully about the consequences of their actions - in particular Syria - but he did not criticise Israel like the majority of Council members.
Syria called for a vote on a draft resolution condemning Israel's "military aggression", but the meeting was adjourned without a vote.
Most Security Council members also condemned a suicide bombing in the coastal town of Haifa on Saturday, which left 19 Israelis dead.
In the West Bank, Palestinian leader Yasser Arafat has appointed an emergency cabinet amid new Israeli threats to expel him following the suicide bombing.
ISRAEL AND SYRIA - OLD FOES
Went to war in 1948, 1967 and 1973
Israeli attacks on Syrian forces in Lebanon go back to 1982, with new strikes in 2001
Israeli warplanes buzzed a presidential palace in Syria in August in what was seen as a warning
Prime Minister-designate Ahmed Qurei says the new cabinet is meant to deal with the crisis situation: "We have a deterioration of the security situation and we need to assert control over security."
Mr Negroponte said there was no need for a new Security Council resolution and that what was needed instead was for Syria to dismantle the terrorism in its borders.
"The United States believes that Syria is on the wrong side of the war on terrorism. We have been clear of the need for Syria to cease harbouring terrorist groups."
UN ambassadors are now consulting their governments on their next steps.
It is unclear when they will next meet, with Mr Negroponte saying there had as yet been no discussion of the timing of any vote.
Syria's draft resolution "strongly condemns the military aggression carried by Israel against the sovereignty and territory of the Syrian Arab Republic".
Syria insists there are no militant training camps on its soil
"We do understand that the main objective of the Israeli Government is to export its internal problems, its failure to achieve any security for the Israelis," the Syrian ambassador to the UN, Fayssal Mekdad, told the BBC's Today programme.
The US has often used its veto to block resolutions condemning Israel because it says others involved in the Middle East conflict should also be included.
Syria and Israel are long-standing enemies, and have been technically at war since Israel's founding in 1948, with tensions further exacerbated by Israel's occupation and illegal annexation of the Golan Heights.
Israel said the target of the air raid was the Ein Saheb training camp, 22 kilometres (14 miles) outside Damascus, which it said was used by several militant Palestinian groups, including Hamas and Islamic Jihad.
Syrian media have described Ein Saheb as a Palestinian refugee camp.
The BBC's Kim Ghattas in Beirut says that, given Syria's obsolete army, diplomacy is Damascus' safest path.
On Sunday, Israelis began burying those killed in the Haifa bombing, including three generations of the Zev Aviv family which lost five family members.
Four children and several Arabs were among the dead. About 50 other people were injured, in what was one of the deadliest suicide attacks since the start of the Palestinian intifada three years ago.