The UN Security Council on Monday "deplored" the killing of an Israeli soldier in a cross-border shooting and called for moves to ease tensions with Lebanon.
A statement agreed by the 15-nation body welcomed action already taken to investigate the killing on Sunday, which Israel has blamed on Lebanese troops.
The Security Council "deplored the shooting of an Israel Defense Forces soldier by a Lebanese Armed Forces soldier" and "called for calm and continued restraint by all parties."
The UN peacekeeping force in south Lebanon said earlier that the killing of the Israeli soldier as he drove near the unofficial border appeared to be "an individual action."
Israeli troops fired across the border in retaliation but officers from the two sides also met to discuss an investigation.
The UN council welcomed statements by the two sides "of their interest in preserving calm and stability" along the border.
UN leader Ban Ki-moon has already called for restraint by Israel and Lebanon. A UN force has patrolled their border area since a brief 2006 war when Israel entered south Lebanon.