In the unanimous declaration, the Security Council's 15 members said they were "outraged" by the attack Saturday claimed by the Syrian branch of Al-Qaeda.
The Security Council called for bringing the perpetrators to justice and asked countries to work with Lebanese authorities to that end.
The council asked "all Lebanese people to preserve national unity in the face of attempts to undermine the country's stability."
It reiterated support for Lebanon's policy of "disassociation" from the conflict in neighboring Syria and the UN's support for Lebanese sovereignty.
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The attack raised fears of a new outbreak of violence in Lebanon's second largest city that has suffered spillover from the Syrian conflict.
Security sources said the bombers were both Lebanese, from a Sunni district of Tripoli known for its sympathy for the rebels fighting to topple the Damascus regime.
The attack occurred in the Jabal Mohsen neighborhood mainly inhabited by members of the Alawite sect of Syrian President Bashar al-Assad.
For years Tripoli has been the site of regular clashes between the mostly Sunni neighborhood of Bab al-Tebbaneh and Jabal Mohsen. The clashes intensified when they were exacerbated by the Syrian conflict.