Ceasefire attempts during the 2006 Lebanon War

The ceasefire attempts during the 2006 Israel-Lebanon conflict started immediately, with Lebanon calling for an immediate and unconditional ceasefire already the day after the start of the hostilities. Israel, however, strongly backed by the United States and the United Kingdom, insisted that there could be no ceasefire until Hezbollah's militia had been disarmed or removed from southern Lebanon. The United Nations Security Council held meetings throughout the conflict but failed to agree on a ceasefire resolution.

The Lebanese Prime Minister Fouad Siniora stated that his government had not been aware of Hezbollah's raid before it happened "and does not take responsibility for, nor endorses what happened on the international border", and Lebanon urged the United Nations to take an immediate decision to stop the firing and lift the Israeli sea and air blockade.

On the same day, the United States vetoed a draft resolution before the Security Council calling for a ceasefire and release of all hostages in relating the Gaza conflict, citing the "fluid and volatile nature of events on the ground" which rendered it outmoded.

BBC News reported that Israeli Prime Minister Ehud Olmert would agree to a ceasefire only if Hezbollah returned the two captured soldiers, stopped firing rockets at Israel, and if Lebanon implemented UN Security Council Resolution 1559, which calls for the group’s disarmament.

The Security Council met to consider the situation. Russia, China, France all condemned Hezbollah's activities but considered Israel's military response to be disproportionate.

U.S. President Bush stated that, "We of course are continuing discussions with Israel, all sovereign nations have a right to defend themselves from terrorist attacks. Our message (to Israel) is defend yourself, but be mindful of the consequences, so we are urging restraint."
On the same day, United Nations Security Council rejected pleas from Lebanon that it call for an immediate ceasefire, the U.S. reportedly being the only member of the 15-nation Council to oppose any action.

...
Wikipedia