Sharon's victory on Thursday came amid violence at home and abroad that left nine Israelis dead, including six people killed when Palestinian gunmen sprayed a Likud polling station with gunfire in northern Israel.
Earlier Thursday in Kenya, three Israelis and nine Kenyans were killed when suicide bombers blew up an Israeli-owned hotel north of Mombasa. About the same time, two missiles barely missed an Israeli plane taking off from Mombasa.
A grim Sharon gave a short victory speech to supporters in Tel Aviv early Friday but said there was no cause for celebration. He accused Palestinian terrorists of trying to influence the Israeli election, and he vowed to hunt down the Kenya attackers.
"The world campaign against terror must become real, tangible and uncompromising, aimed against every terror organization and those who give them shelter everywhere and at all times," Sharon said. His acceptance speech began with a moment of silence for the dead.
"Our long arm will get those who carried out the terror attacks. No one will be forgiven," he said.
The violence overshadowed the polling but didn't alter the anticipated outcome: Surveys in the last week had predicted Sharon would beat Foreign Minister Benjamin Netanyahu by about 20 percentage points.
Sharon took nearly 56 percent of the vote, compared with 40 percent for Netanyahu. A lesser-known challenger, American-born Moshe Feiglin, received about 3 percent, Likud spokesman Shmuel Dahan said. Turnout was about 46 percent of the 300,000 party members entitled to vote.
Netanyahu told supporters late Thursday he had phoned Sharon to congratulate him on his victory and urged the party's members to work together. "We must ensure that the next government will have the power to defeat terror," Netanyahu said.
Sharon will face the new Labor leader, Haifa mayor Mitzna, in Jan. 28 elections, called after Labor bolted the coalition government last month in a dispute over funding for Jewish settlements in the West Bank and Gaza. Polls predict Sharon has good chances of keeping his job, thanks to the Israeli public's shift to a hard-line stance during two years of Israeli-Palestinian fighting.
Since coming to power 21 months ago in the early days of the Palestinian uprising, Sharon has overseen a gradual escalation of military efforts to crush radical Palestinian groups that have waged a terror campaign against Israel.
He sent troops barreling into West Bank cities, destroying much of the Palestinian autonomy government created by the 1990s interim peace accords, removed past peace proposals from the table and refused to deal with Palestinian leader Yasser Arafat - with whom Sharon has had a bitter, decades-old feud.
Netanyahu, who opposes Palestinian independence entirely, had said Sharon's efforts to crush the uprising weren't enough, and he repeatedly called for Arafat to be expelled - a move Sharon has refrained from ordering.
Netanyahu's criticisms helped Sharon position himself as a centrist in comparison - and that could help him against Labor in the general election.
Mitzna's positions are perceived by many to be too conciliatory toward the Palestinians to garner enough support to win over the Israeli center.
Mitzna favors an immediate return to peace talks with the aim of swiftly withdrawing troops and settlers from most of the West Bank and all of Gaza, territories Israel seized in the 1967 Middle East war. He supports a far-reaching settlement with the Palestinians and says he's willing to withdraw from some areas unilaterally if no deal is possible.
Sharon says all violence must stop before peace talks resume. And while he has surprised many by saying he, too, favors a Palestinian state eventually - albeit a restricted one - it seems unlikely he would meet the Palestinians' demands for a state in all the West Bank and Gaza as well as east Jerusalem.
The Al Aqsa Martyrs' Brigade, a militia linked to Palestinian leader Yasser Arafat's Fatah movement, claimed responsibility for the Beit Shean attack, which marred voting in the Likud party primary.
The injured included three sons of David Levy, a former Israeli foreign minister and a top Likud official. One of the sons, Jackie Levy, told Army Radio from the hospital that he saw the gunmen throw at least two grenades toward the crowd.
"I saw the two terrorists getting out of a car, throwing grenades and charging with their guns," he said. "They managed to change magazines a number of times."
Three empty ammunition clips were found at the scene, Army Radio said. A full clip usually holds about 30 bullets.
The mayor of Beit Shean, Pini Caballo, said five Israelis were killed.
"They fired hundreds of bullets," Caballo told Israel Radio. "They went to the Likud branch and saw the crowds and fired in all directions and hit many people."
Rafi Ben-Shetreet, the Likud leader in Beit Shean, said he and others standing at the entrance to the party office heard what sounded like two grenade blasts followed by bursts of shooting. One of the attackers was killed by a security guard, he said.
One of the dead gunman wore an explosives belt that did not detonate, police said. Authorities also were checking whether a stolen car found in the area was carrying explosives.
In a phone call to The Associated Press, the Al Aqsa militia said the attack was a response to the deaths of two militia leaders in an explosion in the West Bank refugee camp of Jenin earlier in the week. The militia has blamed Israel for the deaths, though Israel denied involvement.