The attack, and a rocket strike on a house in southern Israel later in the day, raised the possibility of a fresh round of violence between Hamas militants in Gaza and the Israeli military.
The incidents came just two days after Israel ended an offensive that killed more than 120 Palestinians - and one day after a visit by Secretary of State Condoleezzaof peace talks with Israel.
CBS News correspondent Robert Berger reports that with Israel promising to retaliate for all attacks from Gaza, and the Palestinians demanding restraint, it may be hard for either side to re-launch the negotiations as they vowed to do when Rice was in Jerusalem.
Senior Israeli military officers held an emergency meeting to plot a response, officials said.
Palestinian witnesses said a large explosion tore through the jeep, which was on the Israeli side of the border fence near the Kissufim crossing into central Gaza, and set it on fire.
Several other army vehicles, along with an army helicopter, arrived to rescue the wounded, but came under fire, the witnesses said. Military officials said one of the wounded was in serious condition.
Later Thursday, a rocket fired from Gaza slammed into a house in southern Israeli. Emergency crews were rushing to the scene. There was no immediate word on casualties. Police spokesman Micky Rosenfeld said the attack occurred in Sderot, the southern Israeli border town that has repeatedly been hit by rocket fire in recent years.
Islamic Jihad, a tiny Islamic militant group with links to Iran, claimed responsibility for the ambush and the rocket attack. Hamas, the larger militant group that rules Gaza, said its men also participated in the border attack on the military vehicle.
Abu Ahmad, a spokesman for Islamic Jihad, said the attack was revenge for an Israeli strike a day earlier that killed one of the group's commanders in southern Gaza.
"We are sending our message to all the Zionist criminals," he said. "Your threats to target the leaders of resistance ... won't scare us. We are going to continue our resistance and holy war, and we will continue to rain rockets on your colonies until we make them ghost towns."
For months, Israel has been operating in Gaza against Palestinian militants who fire rockets into southern Israel. Last week, it launched a ground and air offensive in response to especially heavy rocket fire, including several barrages that reached as far as Ashkelon, a city of 120,000, 11 miles north of Gaza.
Israel withdrew its ground forces from northern Gaza on Tuesday, leaving a wide scene of destruction in its wake. Palestinian medical officials say more than half of the dead were civilians. Israel accuses Hamas militants of using civilians for cover.
Palestinian President Mahmoud Abbas suspended peace talks with Israel earlier this week to protest the violence in Gaza. Despite Abbas' rivalry with Hamas, Israeli military action is so unpopular with the Palestinian public that it undermines his authority and makes it difficult for him to negotiate with Israel.
Hamas violently seized control of Gaza from Abbas' forces last June. Abbas wields no control in Gaza, but continues to claim to represent the area's 1.4 million people.
On Wednesday, Abbas said he would not return to the negotiating table until Israel reached a truce in Gaza. However, under pressure from visiting Secretary of State Condoleezza Rice, Abbas backtracked and agreed to resume talks, though it remained unclear when negotiations will restart.
Israel has been negotiating with Abbas, a moderate who rules from the West Bank, since last November. At the same time, it continues to battle the Hamas militants who control the Gaza Strip. Israel has also imposed a painful economic embargo on Gaza, causing widespread hardship in the already impoverished area.
Prime Minister Ehud Olmert's office announced Wednesday that Israel would maintain its pressure on Hamas. Olmert did leave the door open to an unofficial truce with Hamas.
"If there is no rocket fire at Israel, there won't be Israeli attacks on Gaza," he told reporters.
In other violence Thursday, Israeli forces attacked a rocket-launching site in the northern Gaza Strip, killing one militant, Palestinian medics said. The army said it had carried out an air strike on a launching site.
Israel's blockade of Gaza has led to shortages of basic staples, fuel and electricity. On Thursday, a coalition of eight British human rights groups claimed the humanitarian situation in Gaza is at its worst point since Israel captured the territory in 1967. Israel withdrew from Gaza in 2005, but continues to control its borders and airspace.
The report said that more than 1.1 million people, about 80 percent of Gaza's residents, are now dependent on food aid, up from 63 percent in 2006, unemployment is close to 40 percent. Close to 70 percent of the 110,000 workers employed in the private sector have lost their jobs.
It also said that hospitals are suffering from power cuts of up to 12 hours a day, and the water and sewage systems were close to collapse, 10 million to 12 million gallons of sewage pouring into the sea daily.
"Israel has the right and obligation to protect its citizens, but as the occupying power in Gaza it also has a legal duty to ensure that Gazans have access to food, clean water, electricity and medical care," said Amnesty International UK Director Kate Allen, one of groups behind the report.
Israel's Defense Ministry rejected the report, blaming the militant Hamas rulers of Gaza for the hardships. It also said medicine and other humanitarian supplies continue to flow into Gaza.
The 16-page report - sponsored by Amnesty, along with CARE International UK, CAFOD, Christian Aid, Medecins du Monde UK, Oxfam, Save the Children UK and Trocaire - calls on the British government to exert greater pressure on Israel and to reverse its policy on not negotiating with Gaza's Hamas rulers.