The double attack killed at least 23 people and wounded almost 150 and heightened fears that Lebanon will be sucked into Syria's civil war.
The 15-member Security Council and Ban released statements that "strongly condemned" the attack.
The council "appealed to all Lebanese people to preserve national unity in the face of attempts to undermine the country's stability."
It "stressed the importance for all Lebanese parties to respect Lebanon's policy of disassociation and to refrain from any involvement in the Syrian crisis."
"He urges all Lebanese parties to act with restraint and to support the institutions of the state, and particularly the security forces, as they seek to prevent further acts of terrorism."
UN political chief Jeffrey Feltman today highlighted to the UN Security Council reports that Lebanese militia Hezbollah was fighting with President Bashar al-Assad's forces in Syria "in clear violation" of a statement by Lebanese parties to stay out of the war.