Sheikh Hassan Nasrallah, the leader of Hezbollah, said his guerrillas had achieved a "strategic, historic victory" against Israel.
"We came out victorious in a war in which big Arab armies were defeated [before]," he said in a pre-recorded address on Al-Manar television on Monday.
Nasrallah also said that now was not the time to debate the disarmament of Hezbollah fighters, arguing that the issue should be done in secret sessions of the government to avoid serving Israeli interests.
"This is immoral, incorrect and inappropriate," he said. "It is wrong timing on the psychological and moral level particularly before the ceasefire.
"Who will defend Lebanon in case of a new Israeli offensive? The Lebanese army and international troops are incapable of protecting Lebanon."
Moments after his speech ended, celebratory gunfire erupted across Beirut.
Earlier, posters of Nasrallah were distributed in Beirut's Shia-dominant southern suburbs with the caption: "The divine victory."
However, Israel maintained on Monday that it had won a diplomatic victory over Hezbollah because the UN resolution would put the group under international scrutiny.
"We have the diplomatic advantage as Hezbollah is now under the microscope of the international community," Yigal Palmor, a foreign ministry spokesman said.
Hezbollah and its chief, Hassan Nasrallah, "will have to respect resolution 1701", he said, which calls for an embargo on arms and training to fighters in Lebanon.
"This means that there will no longer be a state within a state along our northern border to keep provoking us," he said.
Palmor said: "Politically and militarily, Hezbollah can no longer do what it likes in Lebanon."
Shimon Peres, the deputy prime minister of Israel, said: "Hezbollah will not finish a huge hero, but with its tail between its legs."