Hezbollah chief Hassan Nasrallah says his guerrilla group will fire more rockets further into central Israel.
On Friday, Hezbollah fired rockets 50 kilometers into Israel.
In a televised statement, Nasrallah said Israel has suffered a serious defeat. He spoke shortly after Israeli troops pulled back from the Lebanese border town of Bint Jbail. The Israeli army lost nine soldiers in fighting before taking control of the town this week.
Lebanese officials say an Israeli airstrike killed a woman and at least five children on Saturday. A later strike destroyed Lebanon's main road to Damascus near the Syrian border.
U.N. officials say another Israeli strike hit an observation post, wounding two Indian peacekeepers
And Hezbollah fired more rockets into northern Israel.
Israel also rejected a U.N. call for a 72-hour truce to allow women, children and the elderly to escape the fighting and let emergency aid pass.
Israel says it already has opened humanitarian corridors, and it accuses Hezbollah of blocking aid shipments.
French Foreign Minister Philipe Douste-Blazy says he regrets Israel's refusal and will appeal to Israeli authorities to agree to a humanitarian ceasefire.
Earlier on Saturday, a U.S. boat arrived in Beirut with supplies for hundreds of thousands. The U.N. refugee agency is sending its first convoys of trucks into Lebanon from Syria.