Israel's attacks were in Gaza City, where the most widespread factional fighting in nearly a year between Hamas and the rival Fatah continued Thursday.
The raging street battles have turned the densely populated seaside city into a war zone, endangered the Palestinian unity government and threatened to drag Israel into the fray.
Hamas stepped up the rocket attacks just as the Palestinian infighting intensified, reports CBS News correspondent Robert Berger.
"Hamas killed a lot of fellow Palestinians, some in brutal executions and ambushes, so a good way to divert attention from that was to draw Israel into the fighting," Berger says. "If Hamas is targeted by Israel, it wins immediate sympathy from the public and also unites the Palestinians. Instead of fighting each other, they'll turn their attention to fighting a common enemy — Israel. "
A new cease-fire between the warring Palestinian parties sharply reduced the infighting Thursday. But by mid-afternoon, three people had been killed in new clashes. Nearly two dozen were killed Wednesday.
The Israeli army confirmed the air strikes, which came after Israel threatened "harsh" action in response to repeated Palestinian rocket attacks.
"Israel will defend our citizens. We will actively stop rockets, rocket launchers, those who plan the terror infrastructure," said Israeli government spokeswoman Miri Eisin. She repeated Israel's vow not to be drawn into the Gaza morass, but the heavy air strike raised questions about the commitment.
Hamas said an Israeli aircraft attacked a Palestinian car carrying two senior Hamas commanders, killing one and wounding the other. It did not identify them. The army said that air strike had targeted a Palestinian rocket squad.
The explosion at the Hamas compound sent heavy plumes of gray smoke into the Gaza sky, destroying the structure and several others around it and sending terrified residents scurrying.
After the blast, a large crowd gathered at the site, frantically digging through the rubble and pulling out the wounded. One woman, her white robe covered in blood, was carried away from the area.
Palestinian witnesses and medical officials said one person was killed and 45 in the first air strike.
Hamas said the target was an administration building of its elite bodyguards unit. The two-story structure is normally filled with Hamas personnel.
In the third attack, Israel struck a trailer housing security guards of a senior Hamas official Thursday, killing a Hamas militant, an ambulance driver said. Several other people were injured.
Earlier Thursday, a small number of Israeli tanks edged into the northern Gaza Strip on Thursday, taking up positions near the border fence.
In a text message sent to reporters, Hamas military wing spokesman Abu Obeida vowed revenge against Israel, possibly by suicide bombing.
"The Zionist enemy are launching an open war against Hamas. Therefore, reprisal options are open, including self-sacrifice operations," he said. "We advise the Zionist settlers to go immediately to the basement of their residence because our rockets will not spare any of them."
reports Sderot's terrorized residents are accusing the government of doing nothing.
"We're on the front lines of a war. We have a very strong army, but instead of the army coming to our defense, they're just allowing us to suffer," said one resident.
Israel said its attacks on Hamas were retaliation for dozens of rockets fired by Hamas at Israel over the past few days, reports Berger.
Palestinian President Mahmoud Abbas postponed a planned visit to the Gaza Strip from his West Bank headquarters after the latest outbreak of violence, officials said.
Officials in Abbas' office said the trip would be delayed by at least a day, but gave no firm time for his visit. They said he was determined to travel to Gaza, though the delay appeared to signal that his people could not guarantee his safety.
"The reason for the trip is to stop the fighting," Presidential aide Saeb Erekat said. He said the talks would focus on Abbas' plan to end the infighting and chaos plaguing Gaza. "This is to preserve our social fabric, our society, our internal peace," he said. "Without this, we're doomed."
Sporadic gunfire could be heard in Gaza City on Thursday. But it was nowhere near as intense as Wednesday, when masked gunmen engaged in fierce battles and took over otherwise deserted streets, trapping frightening residents in their homes.
Gaza residents took advantage of the lull to stock up on bread, bottled water, diapers and other basic supplies.
Ghassan Abu al-Qas, a grocery store owner, said business was brisk.
"I have run out of cigarettes and I'm almost out of mineral water. I don't have many diapers left," he said. The only item that wasn't selling was newspapers, he said. "No one has asked to buy newspapers," he said.
But streets were still relatively quiet, and few cars were on the roads because of the large number of roadblocks. At one point, gunfire forced a team of electric workers to halt repairs on power lines, leaving parts of Gaza City without power for a third day.
Nearly 50 people have been killed since Sunday in Palestinian infighting, which has included the most ferocious battles in more than a year of factional clashes. The violence has left the two-month-old Palestinian unity government on the brink of collapse.
In Thursday's violence, gunfire erupted at a Hamas funeral procession Thursday, killing two people and wounding 14 others, Palestinian medical officials said.
The funeral was for two Hamas fighters killed during Wednesday's factional violence. Witnesses said members of the procession were firing their weapons into the air — a custom at Palestinian funerals — when members of a Fatah security force based in a nearby building began firing. The two sides accused each other of starting the battle.
In Gaza City, Hamas said one of its men was kidnapped and executed by security forces loyal to Fatah. There was no comment from Fatah.
The violence has left the fragile unity government in tatters, though Fatah and Hamas leaders have said they hope to preserve the coalition. A main goal of the alliance, formed in March, was to halt months of factional violence, but the unity deal never addressed a key area of dispute — control over Palestinian security forces.
Jordan's King Abdullah II said Thursday he was "very concerned" by the wave of inter-Palestinian fighting in Gaza and warned that more violence will come unless progress is made in the peace process.
"I'm very concerned about the violence in Gaza. It must stop for the sake of the Palestinian people and for the sake of Palestine," Abdullah told a gathering of Israeli, Palestinian and Jordanian peace activists.