The condemnation was contained in a statement read to the press by French UN Ambassador Gerard Araud, who is the rotating council president for December.
"The members of the Security Council deplored the shooting of an Israel Defense Forces soldier by a Lebanese Armed Forces soldier, on December 15 in the vicinity of the Blue Line at Naqoura, and called for calm and continued restraint by all parties," the statement said.
On Sunday, Israel accused a Lebanese soldier of shooting dead one of its soldiers on the Blue Line which separates Lebanon from the Israeli occupied territories.
UN Secretary-General Ban Ki-moon, in a separate statement, also deplored the shooting and called for calm by all the parties concerned.
"The members of the Security Council called upon the Israel Defense Forces and the Lebanese Armed Forces to continue to cooperate with the United Nations Interim Force in Lebanon (UNIFIL) to ascertain the facts related to the incident," the statement said.
"In this regard, Council members welcomed the extraordinary Tripartite meeting convened by UNIFIL on December 16 and the reaffirmation by the parties of their commitment to the cessation of hostilities and of their interest in preserving calm and stability along the Blue Line," the statement said. "Council members also welcomed the reaffirmation by the Lebanese authorities of their full commitment to resolution 1701."
The members of the Security Council noted that UNIFIL confirmed the Lebanese government's preliminary findings which indicate that the shooting was an individual action by a soldier, the statement said.
"They further underlined that it remains a serious contravention of the existing operational rules and procedures as related to resolution 1701," the statement said. "The members of the Security Council looked forward to the completion of UNIFIL and Lebanese's investigations into the incident."
Resolution 1701, which ended the 2006 war between Israel and the Lebanese group Hizbollah, calls for respect for the Blue Line, the disarming of all militias in Lebanon, and an end to arms smuggling in the area.
The Lebanese army said Monday that the shooting incident on Sunday in Ras Nakoura on the Blue Line with Israel was an " individual act."
"An investigation has been launched by a military team and the coordination with the UN Interim Force in Lebanon (UNIFIL) is underway," the army said.
The Lebanese army reiterated "its commitment to the Security Council Resolution 1701 in complete, particularly securing the stability of the border regions in cooperation with the UNIFIL."
Lebanese and Israeli army officers met with the UNIFIL peacekeepers on Monday and discussed concrete steps to strengthen the existing security arrangements along the Blue Line border to prevent the re-occurrence of such incidents.
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