Elsewhere in Gaza, two Palestinian teens were critically wounded by Israeli fire.
The violence came as a senior U.S. envoy, William Burns, met with Israeli Foreign Minister Shimon Peres to try to cement a fragile cease-fire. The soldiers' deaths brought to 12 the number of people killed since the cease-fire took hold last week. Six were Palestinians, and six were Israelis.
The Islamic militant group Hamas claimed responsibility for the explosion, announcing the name of the suicide bomber over mosque loud speakers in Gaza City.
Prime Minister Ariel Sharon's adviser, Raanan Gissin, said the Palestinian Authority had to take immediate action to prevent further attacks on Israelis.
"Our patience is running out. If no action will be taken by them we will have to draw necessary conclusions and take the action ourselves," Gissin said.
However, Sharon was not expected to walk away from the U.S.-backed truce ahead of his meeting with President Bush in Washington next week.
The two soldiers were killed near the Jewish settlement of Dugit in the northern Gaza Strip. The army said an army patrol was passing by an abandoned house and heard Palestinians calling for help, one from inside a jeep with Israeli license plates stuck in sand near the building.
Two soldiers got out of their vehicle to investigate. When they were about 20 yards from the jeep, it exploded, mortally wounding the two and killing the Palestinian inside. A third soldier who remained in the army vehicle was lightly injured from the blast, said Maj. Ran Adam, an Israeli army spokesman in Gaza.
The blast was so powerful that only an axle was left of the rigged jeep. A bloodied helmet lay in the sand nearby. One soldier standing near the wreckage fought back tears as he was comforted by a friend.
Palestinian security officials said soldiers in the area shot tank and heavy machine-gun fire in response, injuring three Palestinians, two moderately and one lightly.
The Israeli army denied that. Soldiers in the area fired only warning shots as Israeli paramedics arrived to evacuate the wounded, Adam said. The injured Palestinians may have been hurt in the blast, he added.
The explosion occurred a few hundred yards from a beach where about 250 Israelis were bathing at the time, Adam said.
Near the Jewish settlement of Ganei Tal, two 18-year-old Palestinians were seriously wounded by army fire, one with a shot to the chest and another with a bullet in the head, Palestinian doctors said.
Palestinian residents said they heard an explosion rior to the shots. The circumstances of the incident were not clear and the army did not immediately comment.
Angered over a series of deadly Palestinian shooting attacks, Jewish settlers went on rampages at several locales in the West Bank on Friday, targeting Palestinians.
A Palestinian was slightly injured in the village of Bourin when settlers threw stones at the fire truck he was driving and settlers burned dozens of olive trees. Israeli soldiers intervened, forcing the settlers to leave the village, witnesses said.
Settlers also threw rocks at Palestinian cars at a main intersection near the West Bank town of Hebron, causing damage. Soldiers dispersed the settler demonstration without having to use force, the army said.
Some 200,000 settlers live among three million Palestinians in the West Bank and Gaza Strip, land Israel captured in the 1967 Middle East war.
The international community considers the settlements illegal. Palestinians view them as an obstacle to building a state and a legitimate target in their uprising.
About 4,000 Palestinians taking part in a rally of the Islamic Jihad movement at a Gaza refugee camp celebrated news of the Israeli soldiers' deaths, witnesses said. Members of the crowd shouted "Allahu Akbar" (God is greatest) and some sht their weapons in the air.
In Hebron, Palestinians threw more than 30 firebombs at Israelis soldiers, the army said. Soldiers fired rubber-coated steel bullets in response.
As the bloodshed persisted, both sides remained skeptical the truce would stick. Israeli and Palestinian security commanders reported no progress in a meeting late Thursday.
Friday's killings raised to 118 the Israeli death toll since September when Palestinians erupted in revolt against Israeli occupation in the West Bank and Gaza after peace talks stalled. At least 462 Palestinians and 13 Israeli Arabs have also died.
In Tel Aviv, Shimon Peres urged Burns in a meeting Friday to press Palestinian leader Yasser Arafat to halt fighting and attacks.
Sharon also called for greater international pressure on the Palestinians.
"If we succeed in bringing pressure (on Arafat) by the United States and other countries that have an influence, that is what should in the end pave the way for a diplomatic arrangement," Sharon told Israel television Friday. The interview was taped before the killing of the two soldiers.
U.S. Secretary of State Colin Powell was to visit the region next week.
Also Friday, the United Nations appealed for $77 million in emergency aid to provide food, medicines and work for more than 200,000 Palestinian refugee families in the West Bank and Gaza Strip.
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