Rantisi told thousands gathered in Gaza's main soccer stadium to mourn the death of Yassin that Hamas will step up its assault on Israelis. "We will fight them everywhere. We will hit them everywhere. We will chase them everywhere. We will teach them lessons in confrontation."
The group's supporters responded by chanting, "We will sacrifice our blood and souls for you." Hamas is the main militant group behind a campaign of suicide bombings against Israel.
Meanwhile, Israel's police minister, Tzahi Hanegbi, warned that "anyone who is involved in terrorism in Gaza or the West Bank ... knows after yesterday's assassination that no one is immune," according to an Associated Press report.
Rantisi opposes any truce with Israel and rejects compromise with Yasser Arafat's Palestinian Authority. The 54-year-old pediatrician spent seven years in Israeli prisons and was expelled to Lebanon for one year in 1992. He was jailed by the Palestinian Authority for 21 months in the late 1990s. Rantisi escaped an Israeli assassination attempt in June.
Khaled Mashaal reportedly will continue to oversee Hamas' political bureau from Damascus, Syria. Mashaal, who is in his late 40s, helped negotiate a truce last summer that temporarily stopped Palestinians attacks on Israel. In 1997, agents from Israel's Mossad injected him with poison darts in Jordan. He survived after Jordan's King Hussein coerced Israel into providing the antidote. In 1999, Mashaal was expelled from Jordan and moved to Syria.
As Hamas named its new leaders, shops and schools in Gaza were shut as part of a three-day mourning period for the slain Hamas leader.
"This is not calm. This is a strike. We won't do any work today. Everyone is angry. We closed the stores, closed everything," an office worker who called himself Ahmed told Reuters.
"There is a feeling of emptiness," he added, calling Yassin "the spirit of the people."
"Ahmed Yassin, we give you all our love and allegiance," said graffiti daubed outside a mourning tent where Palestinians offered condolences as green Hamas flags flew and nationalistic music played.
The Israeli assassination may have been aimed at weakening Hamas to prevent the group from claiming victory if Israel goes ahead with its planned pullout from Gaza. Israel's decision to kill the Hamas founder was partially motivated by "fears that (Israel's pullout from Gaza) would send a message that terrorism pays because Israel is pulling out unilaterally," David Makovsky, senior fellow at the Washington Institute for Near East Policy, told the NewsHour Monday.
It remains unclear what long-term effects Yassin's death will have on Hamas.
Ziad Abu Amr, an expert on Islamic fundamentalism, said the loss is bound to cause organizational challenges for Hamas.
"Yassin was known for his ability to unite different trends within Hamas," he told Reuters. "He was charismatic, mustered a lot of sympathy and was a moderating influence. No successor will have all those qualities."
Hamas leaders said that while Yassin's death was a blow to morale, it would not hamper the group's operations, including its ability to carry out attacks.
"Hamas will continue in the same way Sheik Yassin taught us. Hamas has its infrastructure, its institutions," Ismail Hanieh, a top Yassin aide, told the AP as Hamas leaders formed a reception line at a Gaza City soccer stadium Monday night to greet the thousands of mourners.