Israel appears to be shedding few tears over the killing of Hamas' spiritual leader, but is braced for reprisals.
The Israeli government says it acted to serve peace and security
Prime Minister Ariel Sharon, who is thought to have ordered the killing, described Sheikh Yassin was "one of Israel's greatest enemies".
He described the sheikh as "the greatest arch-murderer of Palestinian terrorism" who sought to "kill Jews everywhere and eliminate... Israel".
Israel had a "natural right" to target Palestinian militants, he said.
In a two-minute address to Likud Party deputies broadcast live on Israeli radio, he also congratulated the forces who carried out the attack.
"The war against terrorism is not over and will continue every day and everywhere," Mr Sharon added.
There were some dissenting voices, arguing not that killing the sheikh was wrong, but that it was likely to cause more problems than it solved.
Opposition Labour Party leader Shimon Peres said he did not believe that killing militant leaders would eliminate terror - on the contrary it "could lead to an escalation of terror".
Another opposition politician and former minister Yossi Beilin warned the government that it was just a matter of time before more Jews died in retaliatory attacks.
Interior Minister Avraham Poraz, of the centrist Shinui party, said: "It was a bad idea because I am afraid of a revenge coming from the Palestinian side, from the Hamas side.
Yassin had been returning from morning prayers at the mosque
"And I am not so optimistic in thinking by this act we'll be able to eliminate Hamas, or to diminish the dangers of Hamas."
Ran Cohen, of the opposition Meretz Party, said he did not think it was "reasonable" for Israel to have killed Sheikh Yassin.
"I think we have to fight against the terrorists, but especially against the suicide bombers not religious leaders," he said.
Bracing for revenge attacks, the Israeli government sealed off the Gaza Strip and the West Bank, and closed all crossings in and out of the occupied territories.
But soundings of Israeli opinion taken by various media suggest most Israeli welcome the assassination.
"At last," a reader from Rehovot near Tel Aviv wrote in an e-mail to BBC News Online.
"To help you understand who was the man, I challenge you to find any footage or speech where Yassin speaks for peace," another Tel Aviv reader wrote.