A resolution adopted unanimously by the council on Wednesday welcomed Annan's recent report, which said a mixed Lebanese and international court should be established - probably outside Lebanon - to try suspects in the February 14, 2005 bombing that killed Rafiq al-Hariri and 22 others.
The council said it was "mindful of the demand of the Lebanese people that all those responsible for the terrorist bombing ... be identified and brought to justice."
Boutros Assaker, the acting secretary-general in Lebanon's foreign ministry, said his government considered the unanimous vote, "coupled with the Lebanese consensus on this subject, as a clear indication of the international community's strong commitment and determination to punish all those involved in this terrorist crime.
"This in turn will deter criminals and will promote security and stability in Lebanon and throughout the region," he told the council after the vote.
A UN investigating team has spent nearly 10 months looking for al-Hariri's killers.
Earlier this month, Serge Brammertz, the new chief investigator, told the council he was cautiously optimistic that new promises by Syria to cooperate, after months of delays, could lead to progress in the probe.
His predecessor had implicated Syrian and Lebanese officials in the explosion in Beirut that killed al-Hariri.
Annan's report is to help identify
the scope of assistance required
Annan's report and Wednesday's resolution were a response to a December 15 Security Council resolution which asked the secretary-general to help the Lebanese government identify the nature and scope of international assistance needed to try anyone charged in the attack that killed al-Hariri.
In the new resolution, the council said it is "willing to continue to assist Lebanon in the search for the truth and in holding all those involved in this terrorist attack accountable".
It welcomed "the common understanding reached between the (UN) Secretariat and the Lebanese authorities on the key issues regarding the establishment and the main features of a possible tribunal."
The resolution requested Annan "to negotiate an agreement with the government of Lebanon aimed at establishing a tribunal of an international character based on the highest international standards of criminal justice".
It asked the secretary-general to take into account the recommendations in his report and the views of council members and to update the council on the progress of negotiations as he deems appropriate.
It also asked him "to submit in a timely manner for the consideration of the council a report on the implementation of this resolution".
Lebanon's Assaker said: "The Lebanese government will spare no effort to conclude the negotiations with the secretary-general as quickly as possible."