With some estimates of 1.2 million Syrians now in Lebanon, the country's UN ambassador Nawaf Salam said the government may have to consider opening camps.
He added that the country would not close its frontier but that it desperately needs international assistance.
"Lebanon will not close its borders. Lebanon will not turn back any refugee, Lebanon will continue to provide assistance to all Syrian refugees, Salam told reporters after the Security Council met to adopt a statement on Lebanon.
"But let's also be clear that Lebanon alone cannot cope with the burden of the refugee crisis. Lebanon needs international support, needs concrete international help to cope with this growing problem."
Lebanon and Jordan say they cannot cope with the fallout from the 26-month-old Syria war and have called for an international conference on the humanitarian crisis.
The United Nations says there are about 600,000 refugees registered in Lebanon. But Salam said there are more than one million Syrians in Lebanon and think tanks such as the Beirut Institute give a figure of 1.2 million.
A Security Council statement proposed by France called for "strong, coordinated international support for Lebanon to help it continue to withstand the multiple current challenges to its security and stability."
With Lebanon's powerful Hezbollah group now fighting alongside President Bashar al-Assad's forces in Syria, there are mounting fears that the conflict could spill over. These fears were heightened by a car bomb in a Hezbollah stronghold in Beirut on Tuesday.
The Security Council statement said there should be international help for the Lebanese Armed Forces to help police the border and made a new appeal for all sides in Lebanon to stay out of the Syria conflict.
But the council said Lebanon needs "assistance on an unprecedented scale" to confront its refugee crisis.
A special fund set up by the United Nations has received only a fraction of the amount appealed for.
"This country is threatened to be engulfed into the Syrian crisis," said France's UN ambassador Gerard Araud.
"It is nearly a miracle that this country has succeeded to resist the pressures and tensions stemming from the Syrian crisis."
Voice of Russia, AFP