In a 20th anniversary message to Hamas TV, Meshal said Hamas would not abandon violence.
"This is our real choice, our trump card, which causes the enemy to succumb to us," he said. "Our people are able to launch a third and fourth uprising until the dawn of victory arrives."
Meshal said Palestinian President Mahmoud Abbas, who controls the West Bank, does not have the mandate to negotiate with Israel.
Also Saturday, Hamas said Palestinian security forces loyal to Abbas had arrested 26 of its members in the West Bank.
"The Palestinian security forces continued the detention campaign that targets Hamas supporters in various cities in the West Bank," Hamas said in a statement faxed to the press.
The statement added that most of the detainees were arrested in the town of Qalqilya.
"The arrests are meant to prevent Hamas from marking its 20th anniversary," the statement said.
Hamas marks its anniversary amid a continuing feud with rival Abbas' Fatah movement. In June, Hamas routed pro-Abbas security forces and took over the Gaza Strip.
Tens of thousands of Hamas supporters gathered Saturday in a sandy lot and nearby streets in a Gaza marking the anniversary. The crowd appeared to be equal in size, if not bigger, than the one marching in support of Hamas' rival, Fatah, in November in the same spot. That rally drew 250,000, a major challenge to Hamas.
"This is the real referendum on the popularity of resistance, the people converging behind Hamas," said Zayed Herzallah, a 28-year old merchant, who brought a van full of young relatives. "Hamas today, after 20 years and after thousands of martyrs, is graduating the fourth generation (of supporters)."
Large pictures of Hamas' leaders, both in Gaza and in exile, were draped across the speakers' podium. A black banner hanging from a nearby building read, in Arabic, English and French: "We will not recognize Israel."
In the crowd were about 50 female members of Hamas' military wing, dressed in long robes and sporting military-style ammunition vests. Some covered their faces with veils, others with ski masks. Several took to the stage, waving green Hamas flags.
Ahead of the rally, tension was rising between Hamas and Fatah. On Friday, Hamas police arrested Omar Al-Ghoul, an adviser to Abbas' prime minister, Salam Fayyad, and seized some of his belongings.
Al-Ghoul was the most senior Fatah politician to be detained since Hamas forces overtook the territory in June.
Also Friday, three people were killed in a mysterious explosion at a Fatah-organized funeral in Gaza City. Witnesses said a man carrying explosives in a jacket accidentally detonated them, while Hamas security said a member of the procession threw a pipe bomb.
Fatah quickly accused Hamas of being behind the explosion, and the Ramallah government announced Saturday a national day of mourning. Hamas denied involvement, and issued orders to question another senior Fatah official in Gaza, Ibrahim Abu Naja, accusing him spreading the rumors. As of Saturday, Abu Naja was not in detention.