The attack hit a Mercedes carrying Mohammed Khalil, Islamic Jihad's top militant leader in southern Gaza, according to a spokesman for the group known as Abu Abdullah.
Health officials said one militant was killed and two other people were wounded in the attack. Palestinian Interior Ministry officials said two were killed and four wounded.
Atef Qatrous, 22, said he was leaving work when he saw a missile hit the car. One of those inside was decapitated and another was badly wounded, he said.
The army confirmed it had launched an airstrike.
Earlier, Israeli troops arrested more than 200 wanted Palestinians in the West Bank following a wave of rockets fired at Israeli towns. Most of those arrested were members of Hamas, the largest Palestinian militant group, and Islamic Jihad, which has been responsible for several deadly attacks on Israel in recent months.
Among those arrested were Hassan Yousef and Mohammed Ghazal, two of the most prominent Hamas leaders in the West Bank, Hamas officials said.
Prime Minister Ariel Sharon said he would use "all means" to crush the militants, but the rapid escalation in violence could damage his chances in a key vote in his Likud Party with deep implications for the future of his government.
U.S. Secretary of State Condoleezza Rice called Palestinian leader Mahmoud Abbas on Saturday evening and urged him to shore up the 7-month-old cease-fire with Israel and prevent the situation from further deteriorating, Palestinian officials said Sunday. Rice also spoke with Israeli leaders, U.S. Ambassador to Israel Richard H. Jones said.
"We understand the terrorists are trying to provoke Israel at this sensitive time, we understand the Israeli position and the response it has taken," Jones said.
After completing its pullout from Gaza two weeks ago after 38 years of occupation, Israel said it would respond harshly to any attacks originating from the tumultuous coastal strip. The government approved the new offensive after Hamas militants in Gaza fired nearly 40 homemade rockets into Israel on Friday and Saturday, slightly wounding six Israelis. No rockets were fired Sunday, the army said.
"There shall be no restrictions on the use of all means to hit the terrorists and the terror organizations, their equipment and their hideouts," Sharon said Sunday. "The order is unequivocal. We do not mean a one-off operation, we mean ongoing activity whose aim is to hit the terrorists."
The violence destroyed the lingering atmosphere of goodwill left over from the Gaza pullout and badly damaged the shaky cease-fire. The attacks also increased the already intense pressure on Abbas to confront militants.
Abbas said Sunday that he asked U.S. officials to pressure Israel to pull back from its offensive.
"We're back to square one. Now we need time to regain calm. Our people need a quiet life and to make a living," he said Sunday.
Later Sunday, Sharon was to address the central committee of his Likud party before it votes whether to hold an early primary election. Likud hard-liners, led by Sharon's party rival Benjamin Netanyahu, were pushing for an early primary in an effort to oust Sharon as punishment for the Gaza pullout.
The current wave of violence could hurt Sharon's chances in the poll. Sharon's allies say that if he loses the Monday vote he might leave the party he helped found three decades ago, call early elections and run at the head of a new centrist party.
Israeli airstrikes overnight hit targets throughout Gaza, including three weapons-storage facilities and a Gaza City school the military said Hamas used to raise funds for attacks, recruit militants and assist families of suicide bombers. Nineteen people were slightly wounded, and the facilities were heavily damaged.
whether Hamas' leaders were in danger, Ziv said: "Let them decide for themselves."
Hamas promised to retaliate.
"All options are open, including striking inside the Zionist entity, which would pay dearly and regret that it took on Hamas as an enemy," said Mushir al-Masri, a Hamas spokesman.
Israeli police sent reinforcements to major cities and were put on their second-highest level of alert against terror attacks.
In Gaza, Palestinian radio stations offered residents advice to prepare for a possible Israeli raid, telling them to keep their windows open, store water and food and dig tunnels to hide in. Psychologists speaking on one station told parents how to help their children cope with the repeated sonic booms made by low-flying Israeli jets Sunday.
However, few Gazans appeared to be preparing for a major assault.
The violence began Friday when an explosion at a Hamas rally in Gaza's Jebaliya refugee camp killed 20 Palestinians.