The Israeli tanks fired shells and attack helicopters fired missiles during the clashes, Palestinian witnesses said.
Islamic Jihad leader was killed and eight militants and three civilians were wounded, none of them seriously, he said.
Islamic Jihad in a statement pledged revenge attacks "in the depths of the Zionist enemy, God willing."
Israeli defense officials said it was a "pinpoint" operation aimed at Gaza militants. It came just a day after Israel ended a destructive and bloody ground operation in northern Gaza against Palestinian rocket squads.
The armored column entered Gaza through the Kissufim crossing, which was the main crossing point for Israeli settlers in Gaza before Israel's 2005 pullout, witnesses said.
The soldiers arrested two Islamic Jihad militants and were pulling out two hours after the incursion, witnesses said. The Israeli military confirmed that the operation was over.
Meanwhile, Secretary of State Condoleezza Rice arrived in the region Tuesday and appealed to Israelis and Palestinians to resume negotiations.
Some Israeli officials are calling for a large-scale invasion of Gaza to stop the rocket attacks, which this week have ranged as far as the coastal city of Ashkelon, 11 miles north of Gaza.
Israeli Foreign Minister Tzipi Livni was quoted as saying that Israel might be forced to send troops back into the territory, but officials in her office clarified that she was referring to a military operation, not reoccupation.
"We cannot afford this kind of extreme Islamic state controlled by Hamas," Livni told foreign diplomats in a meeting in Jerusalem, according to a ministry statement released Tuesday. Israel evacuated Gaza "not in order to come back, but we might find ourselves in a situation that we have no other alternative."
Defense Minister Ehud Barak has said often that a large-scale operation is nearing, indicating that Israel might try to overthrow the Hamas regime.
However, Israeli Prime Minister Ehud Olmert, while warning of severe reprisals against Hamas, has hesitated to order a large invasion, expressing concern about the inevitably high casualties on both sides.
Palestinians fired three rockets at Israel on Tuesday, hitting a house in the battered border town of Sderot. The number of rockets was far fewer than in previous days. Israel carried out several airstrikes in Gaza, killing one militant.
Palestinian President Mahmoud Abbas, who controls a West Bank government that rivals Hamas' Gaza regime, called off talks with Israel on Sunday to protest the exceptionally high death toll from the latest military operation in Gaza.
Speaking at a joint news conference with Rice in the West Bank town of Ramallah, Abbas said "peace and negotiations are our strategic choice" but fell short of announcing a resumption of talks.
"I call on the Israeli government to halt its aggression so the necessary environment can be created to make negotiations succeed, for us and for them, to reach the shores of peace in 2008," Abbas said, referring to the goal of reaching an Israeli-Palestinian peace treaty stated at a U.S.-sponsored Mideast peace conference in November.
Rice called for the resumption of peace talks as soon as possible, saying they were necessary to counter Hamas' influence.
"What we are trying to achieve is not easy ... but I do believe it can be done. We need very much for everybody to be focused on peace," she said.
Referring to Hamas and its opposition to peacemaking, she said: "We won't let them win."
Rice also said Israel should make "a very strong effort to spare innocent life" in Gaza.
Livni told the diplomats on Monday that Abbas' decision to halt the negotiations "shows weakness," signaling to Hamas that its attacks from Gaza could influence Abbas' actions.
In Washington, President Bush said there is "plenty of time" to get a Mideast peace deal in the 10 months before he leaves office.
"This is a process that always has two steps forward and one step back," Bush said after meeting at the White House with Jordan's King Abdullah II. "We just need to make sure that it's just one step back."
