Israel was retaliating for a Hamas suicide bombing in Jerusalem earlier in the week.
A few hours later, Islamic Jihad said it, too, is ending the cease-fire.
"Israel's response was proportionate," said CBS News Consultant Fouad Ajami. "I think it's even in many ways merciful given the brutality that was heaped on the Israelis, and I think it was predictable."
An Israeli helicopter fired five missiles at a gold-colored station wagon in a crowded Gaza City neighborhood Thursday, killing Ismail Abu Shanab and two bodyguards. Fifteen bystanders were hurt.
The missile strike came two days after a Hamas suicide bomber blew himself up on a Jerusalem bus, killing 20 people, including five Americans.
"When children are killed, when religious people are killed, when your streets are unsafe, when your buses are unsafe, no government can sit idly by and pretend that all is well and talk about a road map," Ajami said.
Palestinian Prime Minister Mahmoud Abbas warned that the killing of the Hamas official, Ismail Abu Shanab, is undermining his planned campaign against Palestinian militants. The Palestinian leadership had decided on the clampdown just hours earlier, under intense U.S. pressure.
"This for sure will affect the whole (peace) process and the decision taken (last night) by the Palestinian Authority," he said. Earlier Thursday, he had met with a U.S. envoy, John Wolf, to discuss the next moves.
Israel has routinely targeted members of Hamas' military wing but rarely gone after the group's political leaders. Abu Shanab, who was in his early 50s, a U.S.-educated professor of engineering, was widely regarded as a moderate in the group, and served as a liaison with Abbas during the prime minister's efforts to persuade Hamas to halt attacks.
Israel says the distinction between political and military leaders is insignificant, because both are involved in planning attacks.
Israeli troops hunting terror suspects Thursday also raided three West Bank towns, killed a 16-year-old bystander in a shooting, and destroyed the family home of the bus bomber.
The Israeli reprisals and Palestinian policy shift came in response to the deadliest attack since the launch of the U.S.-backed "road map" peace plan three months ago.
Abbas had shied away from confrontation with Hamas, Islamic Jihad and armed renegades in his own Fatah movement, saying he feared internal fighting.
However, after the Jerusalem bombing, there was mounting pressure, with the United States demanding an immediate crackdown.
"The end of the road map is a cliff that both sides will fall off of," Secretary of State Colin Powell said.
The declaration by the Palestinian militants that the cease-fire is over is no big deal, said Ajami.
"There was no cease-fire. There is no cease-fire for Hamas and Islamic Jihad," he said. "These are terrorists. They're enemies of the peace. They are enemies of Israel."
They are also enemies of the Palestinians, Ajami, a Palestinian-American, said.
"They're enemies of the aspirations of the Palestinian people," the Johns Hopkins professor said. "They are killers. Nothing more and less, and unless the Palestinians shake them off, and unless the Palestinians themselves, the Palestinian security and Palestinian public opinion, come together to thwart these terrorists of Hamas and Islamic Jihad, there shall be no Palestinian future."
In a first step, Abbas has ordered the arrest of all those directly involved in the bombing, and then asked his Cabinet for proposals on a wider clampdown. The ideas raised in the Cabinet meeting, including arrests, a gag order on Hamas and Islamic Jihad spokesmen and the freezing of assets of militant groups, were taken to Yasser Arafat and top PLO officials for approval late Wednesday.
The meeting, which lasted until early Thursday, was at times stormy. Abbas had told his ministers earlier that he would resign if he did not get Arafat's full support for taking action against Hamas and Islamic Jihad, but it was not clear whether he did make the threat in Arafat's presence.
In the end, Abbas and Arafat agreed on a joint statement which said the Palestinian Authority would enforce the rule of law, take control of illegal weapons and end "military displays" by the militants, a reference to marches led by gunmen.
Islamic Jihad and Hamas officials said they were ordered by Palestinian police not to speak to reporters, and many leaders of the two groups had their phones turned off Thursday.
The Palestinian leadership statement did not refer to arrests, which would appear to be a cornerstone of any crackdown, but Palestinian officials said there would be detentions.
"It's a campaign that even in the worst nightmares Hamas and Islamic Jihad never imagined," said Elias Zananiri, a spokesman for Palestinian security chief Mohammed Dahlan. "There's a list of people to be arrested."
Israeli troops Thursday also raided the West Bank towns of Nablus, Jenin and Tulkarem in search of militants. Since the spring of 2002, when Israel reoccupied most of the West Bank, troops have been moving in and out of Palestinian towns repeatedly to arrested wanted men.
In the West Bank city Hebron, troops blew up the home of the Jerusalem bus bomber, a routine punishment intended as deterrent.
Israel had largely suspended such raids after Hamas, Islamic Jihad and Fatah declared a unilateral truce June 29. However, even after the cease-fire, troops continued chasing so-called "ticking bombs" — wanted men suspected of planning new attacks.