Vijay Nambiar, U.N. Secretary General Kofi Annan's special political adviser and the three-person delegation's head, also said "serious obstacles" stand in the way of a comprehensive ceasefire.
The U.N. Security Council had been delaying any action awaiting a briefing by the delegation. The envoys returned to New York July 20 following meetings with many leaders in the Middle East, including in Israel and Lebanon.
"Today a family of five Israelis was killed by Palestinian militants," Nambiar told the U.N. Security Council at the opening of a daylong meeting on the explosion of violence.
"The Council needs to unite to dramatically reduce the devastating toll on civilians, and to quickly develop the framework for a political solution," he said.
Outlining the extent of the destruction, which had already claimed the lives of over 300 Lebanese and 34 Israelis, he said, "We would welcome a united stance by the Security Council."
Nambiar recounted Lebanese Prime Minister Fouad Siniora's statement that Siniora was not in a position to negotiate a ceasefire himself, since he has no involvement in or knowledge of Hezbollah's activities
Israeli leaders stressed Hezbollah's responsibility for initiating the conflict and made clear Israel's decision to continue military operations until Hezbollah was seriously weakened.
Nambiar stressed the international community should work to secure some form of cessation of hostilities as well as to develop quickly the elements of a political framework that would pave the way for a ceasefire.
"A political package is needed that gives the governments of Israel and Lebanon confidence that the horrors each country is now enduring will not be repeated," Nambiar said.