Israeli air strikes, Hezbollah missile attacks and heavy ground combat continued Sunday in Lebanon and Israel as members of the U.N. Security Council continued consideration of a draft resolution to bring about a cease-fire in the conflict. In one incident, Hezbollah rockets killed at least 11 Israeli soldiers in northern Israel. Earlier, Lebanese officials said Israel carried out more air strikes in Lebanon, killing at least 15 people, including one Lebanese military official

Israel carried out air strikes across southern Lebanon and also unleashed the heaviest artillery bombardment of Lebanese border areas so far in the conflict. Hezbollah militants attacked a concentration of Israeli ground troops near the border, in a sign that hostilities could increase before a cease-fire is eventually agreed to.

Isaac Herzog, a member of Israel's security cabinet, says the key to achieving a cease-fire will be the Lebanese government exerting authority over Hezbollah.

"The Lebanese government must make sure that Hezbollah will not breach this agreement," he says.

The resolution being considered by the Security Council calls for Hezbollah to immediately end attacks on Israel and for Israel to immediately stop offensive military operations. It allows for Israel to respond if attacked by Hezbollah.

A second resolution being considered will send international peacekeepers to southern Lebanon.